Daily Papers

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

Scaling reinforcement learning for visual mathematical reasoning requires more than generating harder questions: as data volume grows, the reward labels themselves must remain reliable. Yet existing data pipelines scale supervision while trusting the labeller, and policy-side methods assume the underlying answers are already correct. We instead treat scaling as a verifiable data-construction problem and decouple two axes before any policy update: prompt difficulty, expanded by route-specific evolution operators, and answer reliability, enforced by offline hypothesis-test falsification. We instantiate this as VeriEvol, an iterative framework with two extensible components: a type-aware evolution module that rewrites low-difficulty image-question seeds into harder, image-grounded prompts; and HTV-Agent, a verifier that accepts an answer only after multi-source counter-evidence has failed to refute it. The resulting verified data scales in volume, extends by adding evolution routes or verifier channels, and plugs directly into existing GRPO-style RL recipes. On a five-benchmark visual-math suite, scaling evolved SFT data from 10K to 250K samples raises the mean accuracy from 35.42 to 54.73; then, with backbone, SFT initialization, and GRPO recipe held fixed, VeriEvol adds a cumulative +3.88 over an un-evolved RL baseline, of which +1.82 comes from evolved prompts and +2.06 from the HTV-Agent verifier. We release the prompts, data, models, code, and the full verifier trace of every sample, so that downstream work can scale and audit the pipeline rather than only inspect its outputs.

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Automated theorem proving with large language models in Lean 4 is commonly approached through either step-level tactic prediction with tree search or whole-proof generation. These two paradigms represent opposite granularities for constructing supervised training data: the former provides dense local signals but may fragment coherent proof processes, while the latter preserves global structure but requires complex end-to-end generation. In this paper, we revisit supervision granularity as a training set construction problem over proof trajectories and propose segment-level supervision, a training data construction strategy that extracts locally coherent proof segments for training policy models. We further reuse the same strategy at inference time to trigger short rollouts for existing step-level models. When trained with segment-level supervision on STP, LeanWorkbook, and NuminaMath-LEAN, the resulting policy models achieve proof success rates of 64.84%, 60.90%, and 66.31% on miniF2F, respectively, consistently outperforming both step-level and whole-proof baselines. Goal-aware rollout further improves existing step-level provers while reducing inference costs. It increases the proof success rate of BFS-Prover-V2-7B from 68.77% to 70.74% and that of InternLM2.5-StepProver from 59.59% to 60.33%, showing that appropriate supervision granularity better aligns model learning with proof structure and search. Code and models are available at https://github.com/NJUDeepEngine/SEG-ATP.

LLM-powered tool-calling agents fulfill user requests by interacting with environments, querying data, and invoking tools in a multi-turn process. Yet, most existing benchmarks evaluate these systems under static environment interfaces, with fixed schemas and toolsets, making it difficult to assess how agents behave as environments evolves -- when capabilities are added, reorganized, or deprecated across successive environment versions. In this paper, we study structured environment evolution as a benchmark-construction problem for tool-calling agents. We propose ProEvolve, a graph-based framework that makes environment evolution programmable. At its core, a typed relational graph provides a unified, explicit representation of the environment - data, tools, and schema. Under this formalism, adding, removing, or modifying capabilities are expressed as graph transformations that coherently propagate updates across tools, schemas, and data access. Building on this, ProEvolve supports (1) automatic generation of evolved executable environments through explicit graph transformations, and (2) graph-grounded construction of task sandboxes via subgraph sampling and instantiation. We validate ProEvolve in two tool-calling domains, e-commerce and airline booking, in terms of quality, implementation validity, and failure modes. Finally, we use the generated benchmark as a downstream diagnostic to study how representative agents behave under structured environment evolution.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

In subject-driven text-to-image generation, recent works have achieved superior performance by training the model on synthetic datasets containing numerous image pairs. Trained on these datasets, generative models can produce text-aligned images for specific subject from arbitrary testing image in a zero-shot manner. They even outperform methods which require additional fine-tuning on testing images. However, the cost of creating such datasets is prohibitive for most researchers. To generate a single training pair, current methods fine-tune a pre-trained text-to-image model on the subject image to capture fine-grained details, then use the fine-tuned model to create images for the same subject based on creative text prompts. Consequently, constructing a large-scale dataset with millions of subjects can require hundreds of thousands of GPU hours. To tackle this problem, we propose Toffee, an efficient method to construct datasets for subject-driven editing and generation. Specifically, our dataset construction does not need any subject-level fine-tuning. After pre-training two generative models, we are able to generate infinite number of high-quality samples. We construct the first large-scale dataset for subject-driven image editing and generation, which contains 5 million image pairs, text prompts, and masks. Our dataset is 5 times the size of previous largest dataset, yet our cost is tens of thousands of GPU hours lower. To test the proposed dataset, we also propose a model which is capable of both subject-driven image editing and generation. By simply training the model on our proposed dataset, it obtains competitive results, illustrating the effectiveness of the proposed dataset construction framework.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

The ability to reason, adapt, and creatively solve problems under unexpected challenges is essential for robots operating in real-world environments. However, current robotic benchmarks primarily emphasize skill-level execution and provide limited insight into such cognitive reasoning capabilities. We introduce RoboWits, a bi-manual robotic benchmark designed to systematically evaluate cognitive reasoning, creative tool use, and robustness to unexpected conditions. To enable scalable construction of high-quality reasoning-centric unexpected scenarios, we propose an automated task generation pipeline formulated as a multi-agent cooperative framework, comprising agents for seed task generation and verification, metric generation, scene generation, and task mutation. Using the pipeline, we curated 30 diverse seed tasks and 208 tasks with mutations and graded difficulty across geometry, material, and assembly-based reasoning. We benchmark popular robot policies, pre-trained VLAs, and oracle-state planners. Our results reveal a significant performance gap: while pre-trained VLAs exhibit preliminary success on seed tasks after single-task fine-tuning, they struggle to perform on mutated tasks, implying their brittleness in manipulation tasks requiring reasoning, strategy adaptation, and robustness to deceptive or constrained environments. Project page is available at https://umass-embodied-agi.github.io/RoboWits.

Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches process diagrams as static images, they lack the capacity for dynamic manipulation - a core aspect of human geometric reasoning involving auxiliary line construction and affine transformations. We present GeoSketch, a neural-symbolic framework that recasts geometric reasoning as an interactive perception-reasoning-action loop. GeoSketch integrates: (1) a Perception module that abstracts diagrams into structured logic forms, (2) a Symbolic Reasoning module that applies geometric theorems to decide the next deductive step, and (3) a Sketch Action module that executes operations such as drawing auxiliary lines or applying transformations, thereby updating the diagram in a closed loop. To train this agent, we develop a two-stage pipeline: supervised fine-tuning on 2,000 symbolic-curated trajectories followed by reinforcement learning with dense, symbolic rewards to enhance robustness and strategic exploration. To evaluate this paradigm, we introduce the GeoSketch Benchmark, a high-quality set of 390 geometry problems requiring auxiliary construction or affine transformations. Experiments on strong MLLM baselines demonstrate that GeoSketch significantly improves stepwise reasoning accuracy and problem-solving success over static perception methods. By unifying hierarchical decision-making, executable visual actions, and symbolic verification, GeoSketch advances multimodal reasoning from static interpretation to dynamic, verifiable interaction, establishing a new foundation for solving complex visuospatial problems.

Data contamination in evaluation is getting increasingly prevalent with the emerge of language models pre-trained on super large, automatically-crawled corpora. This problem leads to significant challenges in accurate assessment of model capabilities and generalisations. In this paper, we propose LatestEval, an automatic method leverages the most recent texts to create uncontaminated reading comprehension evaluations. LatestEval avoids data contamination by only using texts published within a recent time window, ensuring no overlap with the training corpora of pre-trained language models. We develop LatestEval automated pipeline to 1) gather latest texts; 2) identify key information, and 3) construct questions targeting the information while removing the existing answers from the context. This encourages models to infer the answers themselves based on the remaining context, rather than just copy-paste. Our experiments demonstrate that language models exhibit negligible memorisation behaviours on LatestEval as opposed to previous benchmarks, suggesting a significantly reduced risk of data contamination and leading to a more robust evaluation. Data and code are publicly available at: https://github.com/liyucheng09/LatestEval.

A coreset is a tiny weighted subset of an input set, that closely resembles the loss function, with respect to a certain set of queries. Coresets became prevalent in machine learning as they have shown to be advantageous for many applications. While coreset research is an active research area, unfortunately, coresets are constructed in a problem-dependent manner, where for each problem, a new coreset construction algorithm is usually suggested, a process that may take time or may be hard for new researchers in the field. Even the generic frameworks require additional (problem-dependent) computations or proofs to be done by the user. Besides, many problems do not have (provable) small coresets, limiting their applicability. To this end, we suggest an automatic practical framework for constructing coresets, which requires (only) the input data and the desired cost function from the user, without the need for any other task-related computation to be done by the user. To do so, we reduce the problem of approximating a loss function to an instance of vector summation approximation, where the vectors we aim to sum are loss vectors of a specific subset of the queries, such that we aim to approximate the image of the function on this subset. We show that while this set is limited, the coreset is quite general. An extensive experimental study on various machine learning applications is also conducted. Finally, we provide a ``plug and play" style implementation, proposing a user-friendly system that can be easily used to apply coresets for many problems. Full open source code can be found at https://github.com/alaamaalouf/AutoCoreset{https://github.com/alaamaalouf/AutoCoreset}. We believe that these contributions enable future research and easier use and applications of coresets.

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

Multimodal large language models are increasingly capable of complex reasoning, yet their performance often degrades when they must externalize a problem through a tool and then reason over the tool's output, specifically when they rely on visual aids. This gap is especially important because real engineering and scientific workflows often rely on visualization tools for analysis, validation, and decision-making. To study this discrepancy, we introduce VAMPS (Visual-Assisted Mathematical Problem Solving), a benchmark for graph-assisted mathematics. VAMPS contains 1,168 multimodal, bilingual multiple-choice question-answer pairs drawn from Iranian University Entrance Exam algebra and calculus problems and expanded with human-reviewed LLM-generated synthetic variants, all selected so that plotting provides a natural solution strategy by revealing intersections, extrema, asymptotes, etc. Designed for both benchmarking and diagnosis, VAMPS goes beyond prior multimodal benchmarks that primarily evaluate reasoning over fixed visual inputs by testing whether a model can benefit from constructing a useful graph and grounding its answer in the resulting visualization. Overall, we found that across a diverse set of models, direct analytical solving surprisingly outperforms tool-enabled visual solving, even on problems where plotting is a natural strategy.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Text-to-SQL aims to translate natural language queries into SQL statements, which is practical as it enables anyone to easily retrieve the desired information from databases. Recently, many existing approaches tackle this problem with Large Language Models (LLMs), leveraging their strong capability in understanding user queries and generating corresponding SQL code. Yet, the parametric knowledge in LLMs might be limited to covering all the diverse and domain-specific queries that require grounding in various database schemas, which makes generated SQLs less accurate oftentimes. To tackle this, we propose constructing the knowledge base for text-to-SQL, a foundational source of knowledge, from which we retrieve and generate the necessary knowledge for given queries. In particular, unlike existing approaches that either manually annotate knowledge or generate only a few pieces of knowledge for each query, our knowledge base is comprehensive, which is constructed based on a combination of all the available questions and their associated database schemas along with their relevant knowledge, and can be reused for unseen databases from different datasets and domains. We validate our approach on multiple text-to-SQL datasets, considering both the overlapping and non-overlapping database scenarios, where it outperforms relevant baselines substantially.

High-definition (HD) maps, particularly those containing lane-level information regarded as ground truth, are crucial for vehicle localization research. Traditionally, constructing HD maps requires highly accurate sensor measurements collection from the target area, followed by manual annotation to assign semantic information. Consequently, HD maps are limited in terms of geographic coverage. To tackle this problem, in this paper, we propose SIO-Mapper, a novel lane-level HD map construction framework that constructs city-scale maps without physical site visits by utilizing satellite images and OpenStreetmap data. One of the key contributions of SIO-Mapper is its ability to extract lane information more accurately by introducing SIO-Net, a novel deep learning network that integrates features from satellite image and OpenStreetmap using both Transformer-based and convolution-based encoders. Furthermore, to overcome challenges in merging lanes over large areas, we introduce a novel lane integration methodology that combines cluster-based and graph-based approaches. This algorithm ensures the seamless aggregation of lane segments with high accuracy and coverage, even in complex road environments. We validated SIO-Mapper on the Naver Labs Open Dataset and NuScenes dataset, demonstrating better performance in various environments including Korea, the United States, and Singapore compared to the state-of-the-art lane-level HD mapconstruction methods.

Generating an image from a provided descriptive text is quite a challenging task because of the difficulty in incorporating perceptual information (object shapes, colors, and their interactions) along with providing high relevancy related to the provided text. Current methods first generate an initial low-resolution image, which typically has irregular object shapes, colors, and interaction between objects. This initial image is then improved by conditioning on the text. However, these methods mainly address the problem of using text representation efficiently in the refinement of the initially generated image, while the success of this refinement process depends heavily on the quality of the initially generated image, as pointed out in the DM-GAN paper. Hence, we propose a method to provide good initialized images by incorporating perceptual understanding in the discriminator module. We improve the perceptual information at the first stage itself, which results in significant improvement in the final generated image. In this paper, we have applied our approach to the novel StackGAN architecture. We then show that the perceptual information included in the initial image is improved while modeling image distribution at multiple stages. Finally, we generated realistic multi-colored images conditioned by text. These images have good quality along with containing improved basic perceptual information. More importantly, the proposed method can be integrated into the pipeline of other state-of-the-art text-based-image-generation models to generate initial low-resolution images. We also worked on improving the refinement process in StackGAN by augmenting the third stage of the generator-discriminator pair in the StackGAN architecture. Our experimental analysis and comparison with the state-of-the-art on a large but sparse dataset MS COCO further validate the usefulness of our proposed approach.

Triple-based Iterative Retrieval-Augmented Generation (iRAG) mitigates document-level noise for multi-hop question answering. However, existing methods still face limitations: (i) greedy single-path expansion, which propagates early errors and fails to capture parallel evidence from different reasoning branches, and (ii) granularity-demand mismatch, where a single evidence representation struggles to balance noise control with contextual sufficiency. In this paper, we propose the Construction-Integration Retrieval and Adaptive Generation model, CIRAG. It introduces an Iterative Construction-Integration module that constructs candidate triples and history-conditionally integrates them to distill core triples and generate the next-hop query. This module mitigates the greedy trap by preserving multiple plausible evidence chains. Besides, we propose an Adaptive Cascaded Multi-Granularity Generation module that progressively expands contextual evidence based on the problem requirements, from triples to supporting sentences and full passages. Moreover, we introduce Trajectory Distillation, which distills the teacher model's integration policy into a lightweight student, enabling efficient and reliable long-horizon reasoning. Extensive experiments demonstrate that CIRAG achieves superior performance compared to existing iRAG methods.

Natural language understanding (NLU) is an essential branch of natural language processing, which relies on representations generated by pre-trained language models (PLMs). However, PLMs primarily focus on acquiring lexico-semantic information, while they may be unable to adequately handle the meaning of constructions. To address this issue, we introduce construction grammar (CxG), which highlights the pairings of form and meaning, to enrich language representation. We adopt usage-based construction grammar as the basis of our work, which is highly compatible with statistical models such as PLMs. Then a HyCxG framework is proposed to enhance language representation through a three-stage solution. First, all constructions are extracted from sentences via a slot-constraints approach. As constructions can overlap with each other, bringing redundancy and imbalance, we formulate the conditional max coverage problem for selecting the discriminative constructions. Finally, we propose a relational hypergraph attention network to acquire representation from constructional information by capturing high-order word interactions among constructions. Extensive experiments demonstrate the superiority of the proposed model on a variety of NLU tasks.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

Building effective knowledge graphs (KGs) for Retrieval-Augmented Generation (RAG) is pivotal for advancing question answering (QA) systems. However, its effectiveness is hindered by a fundamental disconnect: the knowledge graph (KG) construction process is decoupled from its downstream application, yielding suboptimal graph structures. To bridge this gap, we introduce AutoGraph-R1, the first framework to directly optimize KG construction for task performance using Reinforcement Learning (RL). AutoGraph-R1 trains an LLM constructor by framing graph generation as a policy learning problem, where the reward is derived from the graph's functional utility in a RAG pipeline. We design two novel, task-aware reward functions, one for graphs as knowledge carriers and another as knowledge indices. Across multiple QA benchmarks, AutoGraph-R1 consistently enables graph RAG methods to achieve significant performance gains over using task-agnostic baseline graphs. Our work shows it is possible to close the loop between construction and application, shifting the paradigm from building intrinsically ``good'' graphs to building demonstrably ``useful'' ones.

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

Multimodal large language models (MLLMs) still perform poorly on scientific tasks, particularly those requiring multi-step and interpretable reasoning. Their limitations include insufficient scientific reasoning patterns, lack of global coherence in multi-step inference, and the absence of reflective self-correction, making them unreliable in structured scientific contexts. We introduce EduFlow, the first end-to-end framework that covers the full pipeline of educational scientific reasoning, including data selection, MCTS-based trajectory construction, model training, and output optimization. At its core is EduPRM, a process-aware reward model that critiques reasoning steps with tags and justifications. EduPRM is trained via curriculum learning on three complementary supervision sources: MCTS-guided trajectories, error-injected critiques, and teacher-student dialogues, enabling dynamic adaptation to multi-stage problem solving and iterative refinement during inference. We further propose EduMCTS, a domain-adapted search framework that introduces bootstrapping actions specifically designed for educational reasoning, such as a self-reflection mechanism that promotes reflective error correction. It further leverages EduPRM's fine-grained feedback to guide the search toward higher-quality reasoning trajectories. By applying self-consistency and rejection sampling, we constructed EduMCTS-160K, a large-scale dataset of educational reasoning trajectories. Extensive experiments demonstrate that EduFlow enhances reasoning consistency and coherence. Code, data, and models will be released.

Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem proving, which requires rigorous proofs of stated conclusions, and answer construction, which involves hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but struggle with formal verification, while symbolic provers ensure rigor but cannot efficiently handle creative conjecture generation. We introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving. We present ConstructiveBench, a dataset of 3,431 answer-construction problems in various math competitions with verified Lean formalizations. On the ConstructiveBench dataset, ECP improves the accuracy of answer construction from a Chain-of-Thought (CoT) baseline of 14.54% to 45.06% with the gpt-4.1-mini model. Moreover, combined with ECP's constructed answers, the state-of-the-art DeepSeek-Prover-V2-7B model generates correct proofs for 858 of the 3,431 constructive problems in Lean, achieving 25.01% accuracy compared to 9.86% for symbolic-only baselines. Our code and dataset are publicly available at https://github.com/JackSun200312/ECP.

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM), spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expert-inspired framework that decomposes mathematical modeling into four stages: open-ended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88\% improvement over human expert solutions while requiring only 15 minutes and \$0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0\% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot. Our code is available at https://github.com/usail-hkust/LLM-MM-Agent

We present APT, an advanced Large Language Model (LLM)-driven framework that enables autonomous agents to construct complex and creative structures within the Minecraft environment. Unlike previous approaches that primarily concentrate on skill-based open-world tasks or rely on image-based diffusion models for generating voxel-based structures, our method leverages the intrinsic spatial reasoning capabilities of LLMs. By employing chain-of-thought decomposition along with multimodal inputs, the framework generates detailed architectural layouts and blueprints that the agent can execute under zero-shot or few-shot learning scenarios. Our agent incorporates both memory and reflection modules to facilitate lifelong learning, adaptive refinement, and error correction throughout the building process. To rigorously evaluate the agent's performance in this emerging research area, we introduce a comprehensive benchmark consisting of diverse construction tasks designed to test creativity, spatial reasoning, adherence to in-game rules, and the effective integration of multimodal instructions. Experimental results using various GPT-based LLM backends and agent configurations demonstrate the agent's capacity to accurately interpret extensive instructions involving numerous items, their positions, and orientations. The agent successfully produces complex structures complete with internal functionalities such as Redstone-powered systems. A/B testing indicates that the inclusion of a memory module leads to a significant increase in performance, emphasizing its role in enabling continuous learning and the reuse of accumulated experience. Additionally, the agent's unexpected emergence of scaffolding behavior highlights the potential of future LLM-driven agents to utilize subroutine planning and leverage the emergence ability of LLMs to autonomously develop human-like problem-solving techniques.

The K-core of a graph is the unique maximum subgraph within which each vertex connects to K or more other vertices. The optimal K-core attack problem asks to delete the minimum number of vertices from the K-core to induce its complete collapse. A hierarchical cycle-tree packing model is introduced here for this challenging combinatorial optimization problem. We convert the temporally long-range correlated K-core pruning dynamics into locally tree-like static patterns and analyze this model through the replica-symmetric cavity method of statistical physics. A set of coarse-grained belief propagation equations are derived to predict single vertex marginal probabilities efficiently. The associated hierarchical cycle-tree guided attack ({\tt hCTGA}) algorithm is able to construct nearly optimal attack solutions for regular random graphs and Erd\"os-R\'enyi random graphs. Our cycle-tree packing model may also be helpful for constructing optimal initial conditions for other irreversible dynamical processes on sparse random graphs.

Evolutionary program synthesis systems such as AlphaEvolve, OpenEvolve, and ShinkaEvolve offer a new approach to AI-assisted mathematical discovery. These systems utilize teams of large language models (LLMs) to generate candidate solutions to a problem as human readable code. These candidate solutions are then 'evolved' with the goal of improving them beyond what an LLM can produce in a single shot. While existing mathematical applications have mostly focused on problems of establishing bounds (e.g., sphere packing), the program synthesis approach is well suited to any problem where the solution takes the form of an explicit construction. With this in mind, in this paper we explore the use of OpenEvolve for combinatorial bijection discovery. We describe the results of applying OpenEvolve to three bijection construction problems involving Dyck paths, two of which are known and one of which is open. We find that while systems like OpenEvolve show promise as a valuable tool for combinatorialists, the problem of finding novel, research-level bijections remains a challenging task for current frontier systems, reinforcing the need for human mathematicians in the loop. We describe some lessons learned for others in the field interested in exploring the use of these systems.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

We present MoVerse, a real-time video world model that creates an interactively navigable scene from a single narrow-field-of-view image. This setting is challenging because the input observes only a small fraction of the environment, while interactive roaming requires a complete surrounding world, persistent geometry, controllable camera motion, and temporally coherent high-fidelity observations. MoVerse addresses this problem by separating world construction from observation rendering. It first expands the input into a gravity-aligned 360^circ panorama with topology-aware diffusion, closing the missing field of view before 3D reasoning. It then lifts the panorama into a persistent 3D Gaussian scaffold using panoramic geometry-aware residual prediction, yielding a dense and directly renderable spatial memory. Finally, a Gaussian-conditioned video renderer translates scaffold renderings along user-specified camera trajectories into photorealistic video. To make this renderer practical for interaction, we train a bidirectional diffusion teacher for high-quality conditional rendering and distill it into a causal autoregressive student for bounded-latency streaming. This design combines the controllability and long-range consistency of explicit 3D representations with the perceptual quality of generative video models. MoVerse supports real-time scene roaming at 8~FPS on a single NVIDIA RTX~4090 GPU, demonstrating a practical path toward single-image world creation with interactive video output.

While data curation for Vision Language Models (VLMs) is increasingly active, public practice for constructing pretraining mixtures remains largely heuristic: practitioners stack datasets that pass quality filters, set cross-domain ratios by intuition, and lack a principled, attributable criterion for admitting new data, while frontier recipes remain undisclosed. We formulate data construction as a systematic mixture-optimization problem and turn it into a reproducible engineering discipline by decoupling the mixture into two orthogonal sub-problems: inter-class ratios across capabilities and intra-class ratios within a category. For inter-class allocation, we use a single-variable iterative search; for intra-class composition, we apply a multidimensional, dataset-level assessment scoring Quality and Difficulty, and formulate selection as a constrained convex optimization with a diversity objective. The DecoupleMix framework delivers two critical capabilities: guiding what data to collect next and rendering dataset validation a controlled, attributable experiment. Experiments show our approach consistently surpasses heuristic baselines. Moreover, optimal ratios discovered on small-scale proxies transfer seamlessly to larger scales without retuning. Using 80B additional multimodal continue-pretraining tokens, our VLM is competitive with strong open-source models trained with substantially larger multimodal budgets.

The deployment of large language models (LLMs) like ChatGPT and Gemini has shown their powerful natural language generation capabilities. However, these models can inadvertently learn and retain sensitive information and harmful content during training, raising significant ethical and legal concerns. To address these issues, machine unlearning has been introduced as a potential solution. While existing unlearning methods take into account the specific characteristics of LLMs, they often suffer from high computational demands, limited applicability, or the risk of catastrophic forgetting. To address these limitations, we propose a lightweight behavioral unlearning framework based on Retrieval-Augmented Generation (RAG) technology. By modifying the external knowledge base of RAG, we simulate the effects of forgetting without directly interacting with the unlearned LLM. We approach the construction of unlearned knowledge as a constrained optimization problem, deriving two key components that underpin the effectiveness of RAG-based unlearning. This RAG-based approach is particularly effective for closed-source LLMs, where existing unlearning methods often fail. We evaluate our framework through extensive experiments on both open-source and closed-source models, including ChatGPT, Gemini, Llama-2-7b-chat, and PaLM 2. The results demonstrate that our approach meets five key unlearning criteria: effectiveness, universality, harmlessness, simplicity, and robustness. Meanwhile, this approach can extend to multimodal large language models and LLM-based agents.

Large Language Model (LLM)-driven Multi-agent systems (Mas) have recently emerged as a powerful paradigm for tackling complex real-world tasks. However, existing Mas construction methods typically rely on manually crafted interaction mechanisms or heuristic rules, introducing human biases and constraining the autonomous ability. Even with recent advances in adaptive Mas construction, existing systems largely remain within the paradigm of semi-autonomous patterns. In this work, we propose MasHost, a Reinforcement Learning (RL)-based framework for autonomous and query-adaptive Mas design. By formulating Mas construction as a graph search problem, our proposed MasHost jointly samples agent roles and their interactions through a unified probabilistic sampling mechanism. Beyond the accuracy and efficiency objectives pursued in prior works, we introduce component rationality as an additional and novel design principle in Mas. To achieve this multi-objective optimization, we propose Hierarchical Relative Policy Optimization (HRPO), a novel RL strategy that collaboratively integrates group-relative advantages and action-wise rewards. To our knowledge, our proposed MasHost is the first RL-driven framework for autonomous Mas graph construction. Extensive experiments on six benchmarks demonstrate that MasHost consistently outperforms most competitive baselines, validating its effectiveness, efficiency, and structure rationality.

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer D for the total number of nestings. Standard Monte Carlo methods typically cost at least O(varepsilon^{-(2+D)}) and sometimes O(varepsilon^{-2(1+D)}) to obtain an estimator up to varepsilon-error. More advanced methods, such as multilevel Monte Carlo, currently only exist for D = 1. In this paper, we propose a novel Monte Carlo estimator called READ, which stands for "Recursive Estimator for Arbitrary Depth.'' Our estimator has an optimal computational cost of O(varepsilon^{-2}) for every fixed D under suitable assumptions, and a nearly optimal computational cost of O(varepsilon^{-2(1 + delta)}) for any 0 < delta < frac12 under much more general assumptions. Our estimator is also unbiased, which makes it easy to parallelize. The key ingredients in our construction are an observation of the problem's recursive structure and the recursive use of the randomized multilevel Monte Carlo method.

We present the LLM Economist, a novel framework that uses agent-based modeling to design and assess economic policies in strategic environments with hierarchical decision-making. At the lower level, bounded rational worker agents -- instantiated as persona-conditioned prompts sampled from U.S. Census-calibrated income and demographic statistics -- choose labor supply to maximize text-based utility functions learned in-context. At the upper level, a planner agent employs in-context reinforcement learning to propose piecewise-linear marginal tax schedules anchored to the current U.S. federal brackets. This construction endows economic simulacra with three capabilities requisite for credible fiscal experimentation: (i) optimization of heterogeneous utilities, (ii) principled generation of large, demographically realistic agent populations, and (iii) mechanism design -- the ultimate nudging problem -- expressed entirely in natural language. Experiments with populations of up to one hundred interacting agents show that the planner converges near Stackelberg equilibria that improve aggregate social welfare relative to Saez solutions, while a periodic, persona-level voting procedure furthers these gains under decentralized governance. These results demonstrate that large language model-based agents can jointly model, simulate, and govern complex economic systems, providing a tractable test bed for policy evaluation at the societal scale to help build better civilizations.

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

We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area 2.2195cdots.

We introduce a novel reinforcement learning framework of LLM agents named AGILE (AGent that Interacts and Learns from Environments) designed to perform complex conversational tasks with users, leveraging LLMs, memory, tools, and interactions with experts. The agent possesses capabilities beyond conversation, including reflection, tool usage, and expert consultation. We formulate the construction of such an LLM agent as a reinforcement learning (RL) problem, in which the LLM serves as the policy model. We fine-tune the LLM using labeled data of actions and the PPO algorithm. We focus on question answering and release a dataset for agents called ProductQA, comprising challenging questions in online shopping. Our extensive experiments on ProductQA, MedMCQA and HotPotQA show that AGILE agents based on 7B and 13B LLMs trained with PPO can outperform GPT-4 agents. Our ablation study highlights the indispensability of memory, tools, consultation, reflection, and reinforcement learning in achieving the agent's strong performance. Datasets and code are available at https://github.com/bytarnish/AGILE.

Computer-Aided Design (CAD) models are defined by their construction history: a parametric recipe that encodes design intent. However, existing large-scale 3D datasets predominantly consist of boundary representations (B-Reps) or meshes, stripping away this critical procedural information. To address this scarcity, we introduce Zero-to-CAD, a scalable framework for synthesizing executable CAD construction sequences. We frame synthesis as an agentic search problem: by embedding a large language model (LLM) within a feedback-driven CAD environment, our system iteratively generates, executes, and validates code using tools and documentation lookup to promote geometric validity and operation diversity. This agentic approach enables the synthesis of approximately one million executable, readable, editable CAD sequences, covering a rich vocabulary of operations beyond sketch-and-extrude workflows. We also release a curated subset of 100,000 high-quality models selected for geometric diversity. To demonstrate the dataset's utility, we fine-tune a vision-language model on our synthetic data to reconstruct editable CAD programs from multi-view images, outperforming strong baselines, including GPT-5.2, and effectively bootstrapping sequence generation capabilities without real construction-history training data. Zero-to-CAD bridges the gap between geometric scale and parametric interpretability, offering a vital resource for the next generation of CAD AI.

Communications satellite network (CSN), as an integral component of the next generation of communication systems, has the capability to offer services globally. Data transmission in this network primarily relies on two modes: inter-satellite communication and satellite-to-ground station communication. The latter directly impacts the successful reception of data by users. However, due to resource and task limitations, finding a satisfactory solution poses a significant challenge. The communication satellite-ground station network scheduling problem (CS-GSNSP) aims to optimize CSN effectiveness by devising a plan that maximizes link construction time while considering constraints associated with satellite operation modes. The large number of tasks and numerous constraints in the problem result in a time-consuming evaluation of fitness function values. To address this issue, we propose a fuzzy fitness evaluation method (FFEM) that employs fuzzy or real evaluation methods based on individual similarity degrees. Additionally, we introduce an evolutionary algorithm based on FFEM, called evolutionary algorithm based on FFEM (FFEEA), for iteratively searching high-quality network construction schemes. In FFEEA, an adaptive crossover approach is used for efficient population search. Finally, extensive experiments are conducted to demonstrate that our proposed fuzzy fitness evaluation method and other improvement strategies significantly enhance satellite network service time. The study introduces a novel approach to enhance the efficiency of solving combinatorial optimization problems, such as CS-GSNSP, by mitigating the complexity associated with fitness evaluation.

Frontier scientific reasoning is rapidly emerging as a key foundation for advancing AI agents in automated scientific discovery. Deep research agents offer a promising approach to this challenge. These models develop robust problem-solving capabilities through post-training on information-seeking tasks, which are typically curated via knowledge graph construction or iterative web browsing. However, these strategies face inherent limitations in frontier science, where domain-specific knowledge is scattered across sparse and heterogeneous academic sources, and problem solving requires sophisticated computation and reasoning far beyond factual recall. To bridge this gap, we introduce SciResearcher, a fully automated agentic framework for frontier-science data construction. SciResearcher synthesizes diverse conceptual and computational tasks grounded in academic evidence, while eliciting information acquisition, tool-integrated reasoning, and long-horizon capabilities. Leveraging the curated data for supervised fine-tuning and agentic reinforcement learning, we develop SciResearcher-8B, an agent foundation model that achieves 19.46% on the HLE-Bio/Chem-Gold benchmark, establishing a new state of the art at its parameter scale and surpassing several larger proprietary agents. It further achieves 13-15% absolute gains on SuperGPQA-Hard-Biology and TRQA-Literature benchmarks. Overall, SciResearcher introduces a new paradigm for automated data construction for frontier scientific reasoning and offers a scalable path toward future scientific agents.

Agent skills, which consist of reusable strategies that guide agent reasoning and action, have shown strong potential for improving model capability at inference time. However, current skill construction methods treat the problem as one-shot extraction, overlooking a fundamental tension: a skill tailored to the specific task fails to transfer, while the abstracted skill often provides insufficient guidance. We attribute this fragility to the absence of explicit mechanisms for skill specification and generalization. To address this gap, we introduce SkillComposer, a framework that decomposes skill construction into three learnable operations: create, improve, and merge. Trained via systematic rejection sampling recipe, SkillComposer enables language models to self-evolve skills at inference time and supports three deployment modes: offline for building generalized libraries, online for task-specific refinement, and hybrid for combining both. Comprehensive experiments on τ^2-Bench, LiveCodeBench v6, and AppWorld show that SkillComposer consistently outperforms baselines. Our SkillComposer-4B improves a 27B executor by up to +4.5 on agent tasks and +3.4 on code tasks, while generalizing across domains and task types unseen during training. Analysis reveals that merge and improve address orthogonal quality dimensions and that skill composition is a transferable meta-ability, providing a practical recipe for skill-augmented inference.

Recent breakthroughs in the field of language-guided image generation have yielded impressive achievements, enabling the creation of high-quality and diverse images based on user instructions.Although the synthesis performance is fascinating, one significant limitation of current image generation models is their insufficient ability to generate text coherently within images, particularly for complex glyph structures like Chinese characters. To address this problem, we introduce GlyphDraw, a general learning framework aiming to endow image generation models with the capacity to generate images coherently embedded with text for any specific language.We first sophisticatedly design the image-text dataset's construction strategy, then build our model specifically on a diffusion-based image generator and carefully modify the network structure to allow the model to learn drawing language characters with the help of glyph and position information.Furthermore, we maintain the model's open-domain image synthesis capability by preventing catastrophic forgetting by using parameter-efficient fine-tuning techniques.Extensive qualitative and quantitative experiments demonstrate that our method not only produces accurate language characters as in prompts, but also seamlessly blends the generated text into the background.Please refer to our https://1073521013.github.io/glyph-draw.github.io/{project page}. abstract

In Brazil, all legal professionals must demonstrate their knowledge of the law and its application by passing the OAB exams, the national bar exams. The OAB exams therefore provide an excellent benchmark for the performance of legal information systems since passing the exam would arguably signal that the system has acquired capacity of legal reasoning comparable to that of a human lawyer. This article describes the construction of a new data set and some preliminary experiments on it, treating the problem of finding the justification for the answers to questions. The results provide a baseline performance measure against which to evaluate future improvements. We discuss the reasons to the poor performance and propose next steps.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

Most speech-to-text (S2T) translation studies use English speech as a source, which makes it difficult for non-English speakers to take advantage of the S2T technologies. For some languages, this problem was tackled through corpus construction, but the farther linguistically from English or the more under-resourced, this deficiency and underrepresentedness becomes more significant. In this paper, we introduce kosp2e (read as `kospi'), a corpus that allows Korean speech to be translated into English text in an end-to-end manner. We adopt open license speech recognition corpus, translation corpus, and spoken language corpora to make our dataset freely available to the public, and check the performance through the pipeline and training-based approaches. Using pipeline and various end-to-end schemes, we obtain the highest BLEU of 21.3 and 18.0 for each based on the English hypothesis, validating the feasibility of our data. We plan to supplement annotations for other target languages through community contributions in the future.

Combinatorics is central to Olympiad-level mathematical problem solving, requiring deep discrete reasoning, creative constructions, and rigorous structural insight. Recent evidence suggests that even today's strongest frontier models remain uneven on Olympiad combinatorics, revealing a gap in creative mathematical reasoning. We introduce ComBench, an Olympiad-level combinatorics benchmark for evaluating and diagnosing the combinatorial reasoning capabilities of large language models. ComBench contains 100 human-annotated competition-level problems organized around two complementary settings: analysis-centric problems, which primarily require rigorous mathematical arguments, and construction-centric problems, which require explicit constructions in addition to correctness justifications. The evaluation protocol combines rubric-guided proof grading with deterministic construction verification, exposing cases where proof quality and construction validity diverge. Experiments on frontier open- and closed-source models show that ComBench is far from saturated: the strongest model reaches 65.4% overall Avg. and 75.3% overall Best@4. We further find that Rigorous Proof Reasoning and Constructive Realization are distinct capabilities: Kimi-K2.6 trails GPT-5.5 on analysis-centric proof grading but surpasses it on construction-centric Best@4, while Existence and Construction problems remain consistently hardest across representative frontier models.

We present Research Math Agents (RMA), an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets research-level mathematical problems that require long-horizon reasoning, literature grounding, and iterative proof refinement. RMA decomposes research-level proof solving into specialized modules for problem analysis, literature search and understanding, fair comparison, knowledge-bank construction, and proof verification, all coordinated by initializer, proposer, and verifier agents through a shared structured memory. Within this unified framework, these agents operate in a multi-role, multi-round workflow, collaboratively generating, refining, and verifying candidate proofs through iterative feedback. We evaluate RMA on the First Proof benchmark, which consists of ten research-level problems contributed by expert mathematicians across diverse domains. Through comprehensive expert evaluation, RMA outperforms strong baselines on the First Proof benchmark, including GPT-5.2R and Aletheia, solving eight out of ten research problems and producing more logically sound and readable proofs. Our comprehensive ablation studies further show that performance gains arise from the interaction of structured reasoning modules, iterative refinement, and verifier-based feedback, rather than any single component. Our solutions and implementations will be made publicly available upon acceptance.

Gradient-based data selection offers a principled framework for estimating sample utility in large language model (LLM) fine-tuning, but existing methods are mostly designed for offline settings. They are therefore less suited to online fine-tuning, where data arrives sequentially, sample utility is step-dependent, and the effective update geometry is shaped by adaptive optimizers. We propose an optimizer-aware framework for gradient-based online data selection and reweighting in LLM fine-tuning. Our key idea is to view online selection not as static sample ranking, but as shaping the next target-oriented update under the optimizer state. We formulate this as an optimizer-aware update-matching problem, establish its connection to second-order target utility, and show why subset-level construction must account for interactions and redundancy among selected samples. Based on this view, we develop a two-stage Filter-then-Weight algorithm that first filters geometrically useful candidates and then optimizes their coefficients. To make the framework practical for LLMs, we introduce a factorized outer-product gradient representation and optimized matrix computations for long-context data. Experiments show that our method consistently improves convergence and downstream performance over existing online data selection baselines under the same data budget.

Integrating Large Language Models (LLMs) with Knowledge Graphs (KGs) results in complex systems with numerous hyperparameters that directly affect performance. While such systems are increasingly common in retrieval-augmented generation, the role of systematic hyperparameter optimization remains underexplored. In this paper, we study this problem in the context of Cognee, a modular framework for end-to-end KG construction and retrieval. Using three multi-hop QA benchmarks (HotPotQA, TwoWikiMultiHop, and MuSiQue) we optimize parameters related to chunking, graph construction, retrieval, and prompting. Each configuration is scored using established metrics (exact match, F1, and DeepEval's LLM-based correctness metric). Our results demonstrate that meaningful gains can be achieved through targeted tuning. While the gains are consistent, they are not uniform, with performance varying across datasets and metrics. This variability highlights both the value of tuning and the limitations of standard evaluation measures. While demonstrating the immediate potential of hyperparameter tuning, we argue that future progress will depend not only on architectural advances but also on clearer frameworks for optimization and evaluation in complex, modular systems.

While Chain-of-Thought (CoT) prompting boosts Language Models' (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We propose Faithful CoT, a faithful-by-construction framework that decomposes a reasoning task into two stages: Translation (Natural Language query rightarrow symbolic reasoning chain) and Problem Solving (reasoning chain rightarrow answer), using an LM and a deterministic solver respectively. We demonstrate the efficacy of our approach on 10 reasoning datasets from 4 diverse domains. It outperforms traditional CoT prompting on 9 out of the 10 datasets, with an average accuracy gain of 4.4 on Math Word Problems, 1.9 on Planning, 4.0 on Multi-hop Question Answering (QA), and 18.1 on Logical Inference, under greedy decoding. Together with self-consistency decoding, we achieve new state-of-the-art few-shot performance on 7 out of the 10 datasets, showing a strong synergy between faithfulness and accuracy.

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions. We will release the model, data, and symbolic engine to support future research.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

Data scarcity is a long-standing and crucial challenge that hinders quick development of task-oriented dialogue systems across multiple domains: task-oriented dialogue models are expected to learn grammar, syntax, dialogue reasoning, decision making, and language generation from absurdly small amounts of task-specific data. In this paper, we demonstrate that recent progress in language modeling pre-training and transfer learning shows promise to overcome this problem. We propose a task-oriented dialogue model that operates solely on text input: it effectively bypasses explicit policy and language generation modules. Building on top of the TransferTransfo framework (Wolf et al., 2019) and generative model pre-training (Radford et al., 2019), we validate the approach on complex multi-domain task-oriented dialogues from the MultiWOZ dataset. Our automatic and human evaluations show that the proposed model is on par with a strong task-specific neural baseline. In the long run, our approach holds promise to mitigate the data scarcity problem, and to support the construction of more engaging and more eloquent task-oriented conversational agents.

The impressive development of large language models (LLMs) is expanding into the realm of large multimodal models (LMMs), which incorporate multiple types of data beyond text. However, the nature of multimodal models leads to significant expenses in the creation of training data. Furthermore, constructing multilingual data for LMMs presents its own set of challenges due to language diversity and complexity. Therefore, in this study, we propose two cost-effective methods to solve this problem: (1) vocabulary expansion and pretraining of multilingual LLM for specific languages, and (2) automatic and elaborate construction of multimodal datasets using GPT4-V. Based on015 these methods, we constructed a 91K English-Korean-Chinese multilingual, multimodal training dataset. Additionally, we developed a bilingual multimodal model that exhibits excellent performance in both Korean and English, surpassing existing approaches.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Large Language Models (LLMs) have showcased exceptional performance across a wide array of Natural Language Processing (NLP) tasks. Fine-tuning techniques are commonly utilized to tailor pre-trained models to specific applications. While methods like LoRA have effectively tackled GPU memory constraints during fine-tuning, their applicability is often restricted to limited performance, especially on multi-task. On the other hand, Mix-of-Expert (MoE) models, such as Mixtral 8x7B, demonstrate remarkable performance across multiple NLP tasks while maintaining a reduced parameter count. However, the resource requirements of these MoEs still challenging, particularly for consumer-grade GPUs only have limited VRAM. To address these challenge, we propose MixLoRA, an innovative approach aimed at constructing a resource-efficient sparse MoE model based on LoRA. MixLoRA inserts multiple LoRA-based experts within the feed-forward network block of a frozen pre-trained dense model through fine-tuning, employing a commonly used top-k router. Unlike other LoRA based MoE methods, MixLoRA enhances model performance by utilizing independently configurable attention-layer LoRA adapters, supporting the use of LoRA and its variants for the construction of experts, and applying auxiliary load balance loss to address the imbalance problem of the router. In experiments, MixLoRA achieves commendable performance across all evaluation metrics in both single-task and multi-task learning scenarios. Implemented within the m-LoRA framework, MixLoRA enables parallel fine-tuning of multiple mixture-of-experts models on a single 24GB consumer-grade GPU without quantization, thereby reducing GPU memory consumption by 41\% and latency during the training process by 17\%.

QSE is emerging as a critical discipline to make quantum computing accessible to a broader developer community; however, most quantum development environments still require developers to engage with low-level details across the software stack - including problem encoding, circuit construction, algorithm configuration, hardware selection, and result interpretation - making them difficult for classical software engineers to use. To bridge this gap, we present C2|Q>, a hardware-agnostic quantum software development framework that translates specific types of classical specifications into quantum-executable programs while preserving methodological rigor. The framework applies modular SE principles by classifying the workflow into three core modules: an encoder that classifies problems, produces Quantum-Compatible Formats, and constructs quantum circuits, a deployment module that generates circuits and recommends hardware based on fidelity, runtime, and cost, and a decoder that interprets quantum outputs into classical solutions. In evaluation, the encoder module achieved a 93.8% completion rate, the hardware recommendation module consistently selected the appropriate quantum devices for workloads scaling up to 56 qubits. End-to-end experiments on 434 Python programs and 100 JSON problem instances show that the full C2|Q> workflow executes reliably on simulators and can be deployed successfully on representative real quantum hardware, with empirical runs limited to small- and medium-sized instances consistent with current NISQ capabilities. These results indicate that C2|Q> lowers the entry barrier to quantum software development by providing a reproducible, extensible toolchain that connects classical specifications to quantum execution. The open-source implementation of C2|Q> is available at https://github.com/C2-Q/C2Q and as a Python package at https://pypi.org/project/c2q-framework/.

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

Attributed bipartite graphs (ABGs) are an expressive data model for describing the interactions between two sets of heterogeneous nodes that are associated with rich attributes, such as customer-product purchase networks and author-paper authorship graphs. Partitioning the target node set in such graphs into k disjoint clusters (referred to as k-ABGC) finds widespread use in various domains, including social network analysis, recommendation systems, information retrieval, and bioinformatics. However, the majority of existing solutions towards k-ABGC either overlook attribute information or fail to capture bipartite graph structures accurately, engendering severely compromised result quality. The severity of these issues is accentuated in real ABGs, which often encompass millions of nodes and a sheer volume of attribute data, rendering effective k-ABGC over such graphs highly challenging. In this paper, we propose TPO, an effective and efficient approach to k-ABGC that achieves superb clustering performance on multiple real datasets. TPO obtains high clustering quality through two major contributions: (i) a novel formulation and transformation of the k-ABGC problem based on multi-scale attribute affinity specialized for capturing attribute affinities between nodes with the consideration of their multi-hop connections in ABGs, and (ii) a highly efficient solver that includes a suite of carefully-crafted optimizations for sidestepping explicit affinity matrix construction and facilitating faster convergence. Extensive experiments, comparing TPO against 19 baselines over 5 real ABGs, showcase the superior clustering quality of TPO measured against ground-truth labels. Moreover, compared to the state of the arts, TPO is often more than 40x faster over both small and large ABGs.

In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.

Large-scale text-to-image diffusion models, while powerful, suffer from prohibitive computational cost. Existing one-shot network pruning methods can hardly be directly applied to them due to the iterative denoising nature of diffusion models. To bridge the gap, this paper presents OBS-Diff, a novel one-shot pruning framework that enables accurate and training-free compression of large-scale text-to-image diffusion models. Specifically, (i) OBS-Diff revitalizes the classic Optimal Brain Surgeon (OBS), adapting it to the complex architectures of modern diffusion models and supporting diverse pruning granularity, including unstructured, N:M semi-structured, and structured (MHA heads and FFN neurons) sparsity; (ii) To align the pruning criteria with the iterative dynamics of the diffusion process, by examining the problem from an error-accumulation perspective, we propose a novel timestep-aware Hessian construction that incorporates a logarithmic-decrease weighting scheme, assigning greater importance to earlier timesteps to mitigate potential error accumulation; (iii) Furthermore, a computationally efficient group-wise sequential pruning strategy is proposed to amortize the expensive calibration process. Extensive experiments show that OBS-Diff achieves state-of-the-art one-shot pruning for diffusion models, delivering inference acceleration with minimal degradation in visual quality.

Large language models (LLMs) are displaying emergent abilities for math reasoning tasks,and there is a growing attention on enhancing the ability of open-source LLMs through supervised fine-tuning (SFT).In this paper, we aim to explore a general data strategy for supervised data to help optimize and expand math reasoning ability.Firstly, we determine the ability boundary of reasoning paths augmentation by identifying these paths' minimal optimal set.Secondly, we validate that different abilities of the model can be cumulatively enhanced by Mix of Minimal Optimal Sets of corresponding types of data, while our models MMOS achieve SOTA performance on series base models under much lower construction costs.Besides, we point out GSM-HARD is not really hard and today's LLMs no longer lack numerical robustness.Also, we provide an Auto Problem Generator for robustness testing and educational applications.Our code and data are publicly available at https://github.com/cyzhh/MMOS.

Proof-of-Work (PoW) consensus mechanism is popular among current blockchain systems, which leads to an increasing concern about the tremendous waste of energy due to massive meaningless computation. To address this issue, we propose a novel and energy-efficient blockchain system, CrowdMine, which exploits useful crowdsourcing computation to achieve decentralized consensus. CrowdMine solves user-proposed computing tasks and utilizes the computation committed to the task solving process to secure decentralized on-chain storage. With our designed ``Proof of Crowdsourcing Work'' (PoCW) protocol, our system provides an efficient paradigm for computation and storage in a trustless and decentralized environment. We further show that the system can defend against potential attacks on blockchain, including the short-term 51\% attack, the problem-constructing attack, and the solution-stealing attack. We also implement the system with 40 distributed nodes to demonstrate its performance and robustness. To the best of our knowledge, this is the first system that enables decentralized Proof of Useful Work (PoUW) with general user-proposed tasks posted in a permissionless and trustless network.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

Issue resolution, a complex Software Engineering (SWE) task integral to real-world development, has emerged as a compelling challenge for artificial intelligence. The establishment of benchmarks like SWE-bench revealed this task as profoundly difficult for large language models, thereby significantly accelerating the evolution of autonomous coding agents. This paper presents a systematic survey of this emerging domain. We begin by examining data construction pipelines, covering automated collection and synthesis approaches. We then provide a comprehensive analysis of methodologies, spanning training-free frameworks with their modular components to training-based techniques, including supervised fine-tuning and reinforcement learning. Subsequently, we discuss critical analyses of data quality and agent behavior, alongside practical applications. Finally, we identify key challenges and outline promising directions for future research. An open-source repository is maintained at https://github.com/DeepSoftwareAnalytics/Awesome-Issue-Resolution to serve as a dynamic resource in this field.

In recent times, a plethora of Large Code Generation Models (LCGMs) have been proposed, showcasing significant potential in assisting developers with complex programming tasks. Benchmarking LCGMs necessitates the creation of a set of diverse programming problems, and each problem comprises the prompt (including the task description), canonical solution, and test inputs. The existing methods for constructing such a problem set can be categorized into two main types: manual methods and perturbation-based methods. However, manual methods demand high effort and lack scalability, while also risking data integrity due to LCGMs' potentially contaminated data collection, and perturbation-based approaches mainly generate semantically homogeneous problems with the same canonical solutions and introduce typos that can be easily auto-corrected by IDE, making them ineffective and unrealistic. In this work, we propose the idea of programming problem merging (PPM) and provide two implementation of this idea, we utilize our tool on two widely-used datasets and compare it against nine baseline methods using eight code generation models. The results demonstrate the effectiveness of our tool in generating more challenging, diverse, and natural programming problems, comparing to the baselines.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

The frontier of mathematics is defined by problems whose solutions are not yet known, yet it remains unclear whether language models can meaningfully engage with such problems without human intervention. A major obstacle is the lack of large-scale research-level math datasets. To this end, we introduce ResearchMath-14k, a set of 14{,}056 problems curated from academic sources via a multi-agent pipeline, making it the largest collection of research-level mathematical problems to date. We further generate ResearchMath-Reasoning, 220K teacher trajectories from two open models, where we observe recurring avoidance behaviors such as non-attempts and fabricated references. Interestingly, across eight open-weight models, newer generations produce 5.6times more references and 5.0times more fake references per trace. After agentic filtering of ResearchMath-Reasoning, fine-tuning Qwen3 models from 4B to 30B parameters improves over base models by 9.2 points on average. This shows that filtered open-problem attempts can provide useful supervision even without fully correct reasoning traces. We make ResearchMath-14k publicly available for future works on research-level mathematical reasoning.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

The advancement of reasoning capabilities in Large Language Models (LLMs) requires substantial amounts of high-quality reasoning data, particularly in mathematics. Existing data synthesis methods, such as data augmentation from annotated training sets or direct question generation based on relevant knowledge points and documents, have expanded datasets but face challenges in mastering the inner logic of the problem during generation and ensuring the verifiability of the solutions. To address these issues, we propose RV-Syn, a novel Rational and Verifiable mathematical Synthesis approach. RV-Syn constructs a structured mathematical operation function library based on initial seed problems and generates computational graphs as solutions by combining Python-formatted functions from this library. These graphs are then back-translated into complex problems. Based on the constructed computation graph, we achieve solution-guided logic-aware problem generation. Furthermore, the executability of the computational graph ensures the verifiability of the solving process. Experimental results show that RV-Syn surpasses existing synthesis methods, including those involving human-generated problems, achieving greater efficient data scaling. This approach provides a scalable framework for generating high-quality reasoning datasets.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.

Automating planning with LLMs presents transformative opportunities for traditional industries, yet remains underexplored. In commercial construction, the complexity of automated scheduling often requires manual intervention to ensure precision. We propose CONSTRUCTA, a novel framework leveraging LLMs to optimize construction schedules in complex projects like semiconductor fabrication. CONSTRUCTA addresses key challenges by: (1) integrating construction-specific knowledge through static RAG; (2) employing context-sampling techniques inspired by architectural expertise to provide relevant input; and (3) deploying Construction DPO to align schedules with expert preferences using RLHF. Experiments on proprietary data demonstrate performance improvements of +42.3% in missing value prediction, +79.1% in dependency analysis, and +28.9% in automated planning compared to baseline methods, showcasing its potential to revolutionize construction workflows and inspire domain-specific LLM advancements.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

We advocate for a strong integration of Computational Creativity (CC) with research in large language and vision models (LLVMs) to address a key limitation of these models, i.e., creative problem solving. We present preliminary experiments showing how CC principles can be applied to address this limitation. Our goal is to foster discussions on creative problem solving in LLVMs and CC at prestigious ML venues. Our code is available at: https://github.com/lnairGT/creative-problem-solving-LLMs

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

Recognizing safety violations in construction environments is critical yet remains underexplored in computer vision. Existing models predominantly rely on 2D object detection, which fails to capture the complexities of real-world violations due to: (i) an oversimplified task formulation treating violation recognition merely as object detection, (ii) inadequate validation under realistic conditions, (iii) absence of standardized baselines, and (iv) limited scalability from the unavailability of synthetic dataset generators for diverse construction scenarios. To address these challenges, we introduce Safe-Construct, the first framework that reformulates violation recognition as a 3D multi-view engagement task, leveraging scene-level worker-object context and 3D spatial understanding. We also propose the Synthetic Indoor Construction Site Generator (SICSG) to create diverse, scalable training data, overcoming data limitations. Safe-Construct achieves a 7.6% improvement over state-of-the-art methods across four violation types. We rigorously evaluate our approach in near-realistic settings, incorporating four violations, four workers, 14 objects, and challenging conditions like occlusions (worker-object, worker-worker) and variable illumination (back-lighting, overexposure, sunlight). By integrating 3D multi-view spatial understanding and synthetic data generation, Safe-Construct sets a new benchmark for scalable and robust safety monitoring in high-risk industries. Project Website: https://Safe-Construct.github.io/Safe-Construct

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

Agents are widely deployed as assistants over documents, tools, and code. However, they typically act only on explicit user requests, which surface only the problems the user has noticed, while many other important problems coexist, hidden in plain sight, within the broader user context, with their total number unknown in advance. We frame this as the task of discovering multiple hidden problems from context, in which coexisting problems should be uncovered, grounded in supporting evidence, and paired with concrete actions. To this end, we introduce TIDE, a template-guided iterative framework with two complementary mechanisms. Specifically, motivated by the observation that single-pass prediction anchors on the most salient cases and yields generic claims, we propose iterative discovery, which surfaces a small batch of candidates per round while conditioning on what has already been found, so subsequent rounds extend coverage; and thought templates, reusable schemas distilled from previously solved cases that specify what contextual signals to attend to and how to connect them, anchoring each prediction in a recognizable problem class. We validate TIDE on two realistic settings, personal workspaces and software repositories, across four model backbones, showing substantial gains over single-shot and parallel multi-agent baselines on task coverage, identification, and resolution.

Our work presents a novel angle for evaluating language models' (LMs) mathematical abilities, by investigating whether they can discern skills and concepts enabled by math content. We contribute two datasets: one consisting of 385 fine-grained descriptions of K-12 math skills and concepts, or standards, from Achieve the Core (ATC), and another of 9.9K problems labeled with these standards (MathFish). Working with experienced teachers, we find that LMs struggle to tag and verify standards linked to problems, and instead predict labels that are close to ground truth, but differ in subtle ways. We also show that LMs often generate problems that do not fully align with standards described in prompts. Finally, we categorize problems in GSM8k using math standards, allowing us to better understand why some problems are more difficult to solve for models than others.

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

In this case study, the renowned Travelling Salesmen problem has been studied. Travelling Salesman problem is a most demanding computational problem in Computer Science. The Travelling Salesmen problem has been solved by two different ways using Hopfield Network. The main theory of the problem is to find distance and connectedness between nodes in a graph having edges between the nodes. The basic algorithm used for this problem is Djikstra's Algorithm. But till now , a number of such algorithms have evolved. Among them(some other algorithms) , are distinct and have been proved to solve the travelling salesmen problem by graph theory.

Coding problems are problems that require a solution in the form of a computer program. Coding problems are popular among students and professionals as it enhances their skills and career opportunities. An AI system that would help those who practice coding problems would be highly useful and there is a huge potential for such a system. In this work, we propose a model which uses stacking of hyperparameter tuned boosting models to achieve impressive metric scores of 77.8% accuracy and 0.815 PR-AUC on the dataset that was scraped from Codeforces and Leetcode. We open source the dataset and the models developed for this work.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

Large Reasoning Models (LRMs) have shown impressive capabilities in complex problem-solving, often benefiting from training on difficult mathematical problems that stimulate intricate reasoning. Recent efforts have explored automated synthesis of mathematical problems by prompting proprietary models or large-scale open-source models from seed data or inherent mathematical concepts. However, scaling up these methods remains challenging due to their high computational/API cost, complexity of prompting, and limited difficulty level of the generated problems. To overcome these limitations, we propose ScaleDiff, a simple yet effective pipeline designed to scale the creation of difficult problems. We efficiently identify difficult problems from existing datasets with only a single forward pass using an adaptive thinking model, which can perceive problem difficulty and automatically switch between "Thinking" and "NoThinking" modes. We then train a specialized difficult problem generator (DiffGen-8B) on this filtered difficult data, which can produce new difficult problems in large scale, eliminating the need for complex, per-instance prompting and its associated high API costs. Fine-tuning Qwen2.5-Math-7B-Instruct on the ScaleDiff-Math dataset yields a substantial performance increase of 11.3% compared to the original dataset and achieves a 65.9% average accuracy on AIME'24, AIME'25, HMMT-Feb'25, BRUMO'25, and MATH500, outperforming recent strong LRMs like OpenThinker3. Notably, this performance is achieved using the cost-efficient Qwen3-8B model as a teacher, demonstrating that our pipeline can effectively transfer advanced reasoning capabilities without relying on larger, more expensive teacher models. Furthermore, we observe a clear scaling phenomenon in model performance on difficult benchmarks as the quantity of difficult problems increases. Code: https://github.com/QizhiPei/ScaleDiff.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

Recent methods have demonstrated that Large Language Models (LLMs) can solve reasoning tasks better when they are encouraged to solve subtasks of the main task first. In this paper we devise a similar strategy that breaks down reasoning tasks into a problem decomposition phase and a problem solving phase and show that the strategy is able to outperform a single stage solution. Further, we hypothesize that the decomposition should be easier to distill into a smaller model compared to the problem solving because the latter requires large amounts of domain knowledge while the former only requires learning general problem solving strategies. We propose methods to distill these two capabilities and evaluate their impact on reasoning outcomes and inference cost. We find that we can distill the problem decomposition phase and at the same time achieve good generalization across tasks, datasets, and models. However, it is harder to distill the problem solving capability without losing performance and the resulting distilled model struggles with generalization. These results indicate that by using smaller, distilled problem decomposition models in combination with problem solving LLMs we can achieve reasoning with cost-efficient inference and local adaptation.

We introduce FrontierScience, a benchmark evaluating expert-level scientific reasoning in frontier language models. Recent model progress has nearly saturated existing science benchmarks, which often rely on multiple-choice knowledge questions or already published information. FrontierScience addresses this gap through two complementary tracks: (1) Olympiad, consisting of international olympiad problems at the level of IPhO, IChO, and IBO, and (2) Research, consisting of PhD-level, open-ended problems representative of sub-tasks in scientific research. FrontierScience contains several hundred questions (including 160 in the open-sourced gold set) covering subfields across physics, chemistry, and biology, from quantum electrodynamics to synthetic organic chemistry. All Olympiad problems are originally produced by international Olympiad medalists and national team coaches to ensure standards of difficulty, originality, and factuality. All Research problems are research sub-tasks written and verified by PhD scientists (doctoral candidates, postdoctoral researchers, or professors). For Research, we introduce a granular rubric-based evaluation framework to assess model capabilities throughout the process of solving a research task, rather than judging only a standalone final answer.

Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive results, especially when combined with self-consistency. Nonetheless, some tasks remain particularly difficult for LLMs to solve. Tree of Thoughts (ToT) and Graph of Thoughts (GoT) emerged as alternatives, dividing the complex problem into paths of subproblems. In this paper, we propose Tree of Problems (ToP), a simpler version of ToT, which we hypothesise can work better for complex tasks that can be divided into identical subtasks. Our empirical results show that our approach outperforms ToT and GoT, and in addition performs better than CoT on complex reasoning tasks. All code for this paper is publicly available here: https://github.com/ArmelRandy/tree-of-problems.

Constraint programming is known for being an efficient approach for solving combinatorial problems. Important design choices in a solver are the branching heuristics, which are designed to lead the search to the best solutions in a minimum amount of time. However, developing these heuristics is a time-consuming process that requires problem-specific expertise. This observation has motivated many efforts to use machine learning to automatically learn efficient heuristics without expert intervention. To the best of our knowledge, it is still an open research question. Although several generic variable-selection heuristics are available in the literature, the options for a generic value-selection heuristic are more scarce. In this paper, we propose to tackle this issue by introducing a generic learning procedure that can be used to obtain a value-selection heuristic inside a constraint programming solver. This has been achieved thanks to the combination of a deep Q-learning algorithm, a tailored reward signal, and a heterogeneous graph neural network architecture. Experiments on graph coloring, maximum independent set, and maximum cut problems show that our framework is able to find better solutions close to optimality without requiring a large amounts of backtracks while being generic.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

Mathematics is often perceived as a complex subject by students, leading to high failure rates in exams. To improve Mathematics skills, it is important to provide sample questions for students to practice problem-solving. Manually creating Math Word Problems (MWPs) is time consuming for tutors, because they have to type in natural language while adhering to grammar and spelling rules of the language. Existing Deep Learning techniques for MWP generation either require a tutor to provide the initial portion of the MWP, and/or additional information such as an equation. In this paper, we present an MWP generation system based on Large Language Models (LLMs) that overcome the need for additional input - the only input to our system is the number of MWPs needed, the grade and the type of question (e.g. addition, subtraction). Unlike the existing LLM-based solutions for MWP generation, we carried out an extensive set of experiments involving different LLMs, prompting strategies, techniques to improve the diversity of questions, as well as techniques that employ human feedback to improve LLM performance. Human and automated evaluations confirmed that the generated MWPs are high in quality, with minimal spelling and grammar issues. However, LLMs still struggle to generate questions that adhere to the specified grade and question type requirements.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.

We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannian gradient descent optimization. Experiments on synthetic data sets and a real-world single-cell transcriptomic data show that RHS outperforms Minimum Spanning Tree (MST), Neighbour Joining, and vanilla HyperSteiner (HS). In near-boundary configurations, RHS can achieve a 32% reduction in total length over HS, demonstrating its effectiveness and robustness in diverse data regimes.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

Construction grammar posits that children acquire constructions (form-meaning pairings) from the statistics of their environment. Recent work supports this hypothesis by showing sensitivity to constructions in pretrained language models (PLMs), including one recent study (Rozner et al., 2025) demonstrating that constructions shape the PLM's output distribution. However, models under study have generally been trained on developmentally implausible amounts of data, casting doubt on their relevance to human language learning. Here we use Rozner et al.'s methods to evaluate constructional learning in models from the 2024 BabyLM challenge. Our results show that even when trained on developmentally plausible quantities of data, models represent diverse constructions, even hard cases that are superficially indistinguishable. We further find correlational evidence that constructional performance may be functionally relevant: models that better represent constructions perform better on the BabyLM benchmarks.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for training large language models (LLMs) on complex reasoning tasks, such as mathematical problem solving. A prerequisite for the scalability of RLVR is a high-quality problem set with precise and verifiable answers. However, the scarcity of well-crafted human-labeled math problems and limited-verification answers in existing distillation-oriented synthetic datasets limit their effectiveness in RL. Additionally, most problem synthesis strategies indiscriminately expand the problem set without considering the model's capabilities, leading to low efficiency in generating useful questions. To mitigate this issue, we introduce a Self-aware Weakness-driven problem Synthesis framework (SwS) that systematically identifies model deficiencies and leverages them for problem augmentation. Specifically, we define weaknesses as questions that the model consistently fails to learn through its iterative sampling during RL training. We then extract the core concepts from these failure cases and synthesize new problems to strengthen the model's weak areas in subsequent augmented training, enabling it to focus on and gradually overcome its weaknesses. Without relying on external knowledge distillation, our framework enables robust generalization byempowering the model to self-identify and address its weaknesses in RL, yielding average performance gains of 10.0% and 7.7% on 7B and 32B models across eight mainstream reasoning benchmarks.

The ability to solve problems is a hallmark of intelligence and has been an enduring goal in AI. AI systems that can create programs as solutions to problems or assist developers in writing programs can increase productivity and make programming more accessible. Recently, pre-trained large language models have shown impressive abilities in generating new codes from natural language descriptions, repairing buggy codes, translating codes between languages, and retrieving relevant code segments. However, the evaluation of these models has often been performed in a scattered way on only one or two specific tasks, in a few languages, at a partial granularity (e.g., function) level and in many cases without proper training data. Even more concerning is that in most cases the evaluation of generated codes has been done in terms of mere lexical overlap rather than actual execution whereas semantic similarity (or equivalence) of two code segments depends only on their ``execution similarity'', i.e., being able to get the same output for a given input.

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.

A key component of creativity is associative reasoning: the ability to draw novel yet meaningful connections between concepts. We introduce CREATE, a benchmark designed to evaluate models' capacity for creative associative reasoning. CREATE requires models to generate sets of paths connecting concepts in a model's parametric knowledge. Paths should have high specificity (distinctiveness and closeness of the concept connection) and high diversity (dissimilarity from other paths), and models are scored more highly if they produce a larger set of strong, diverse paths. This task shares demands of real creativity tasks like hypothesis generation, including an extremely large search space, but enables collection of a sizable benchmark with objective answer grading. Evaluation of frontier models shows that the strongest models achieve higher creative utility than others, with the high multiplicity of answers and complexity of the search making benchmark saturation difficult to achieve. Furthermore, our results illustrate that thinking models are not always more effective on our task, even with high token budgets. Recent approaches for creative prompting give some but limited additional improvement. CREATE provides a sandbox for developing new methods to improve models' capacity for associative creativity.

In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, additional attributes are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes can be insufficiently covered by existing training schemes of diffusion generative models, potentially limiting test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses asynchronous time steps for different dimensions and attributes, thus allowing for varying degrees of control over them. Our code is available at: https://github.com/Xrvitd/ComboStoc

Typically, machine learning systems solve new tasks by training on thousands of examples. In contrast, humans can solve new tasks by reading some instructions, with perhaps an example or two. To take a step toward closing this gap, we introduce a framework for developing NLP systems that solve new tasks after reading their descriptions, synthesizing prior work in this area. We instantiate this framework with a new English language dataset, ZEST, structured for task-oriented evaluation on unseen tasks. Formulating task descriptions as questions, we ensure each is general enough to apply to many possible inputs, thus comprehensively evaluating a model's ability to solve each task. Moreover, the dataset's structure tests specific types of systematic generalization. We find that the state-of-the-art T5 model achieves a score of 12% on ZEST, leaving a significant challenge for NLP researchers.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. While several prior works have investigated solving elementary mathematics using LLMs, this work explores the frontier of using GPT-4 for solving more complex and challenging math problems. We evaluate various ways of using GPT-4. Some of them are adapted from existing work, and one is \MathChat, a conversational problem-solving framework newly proposed in this work. We perform the evaluation on difficult high school competition problems from the MATH dataset, which shows the advantage of the proposed conversational approach.

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining the reliability. Prior studies of LLM reliability have primarily focused on knowledge tasks to identify unanswerable questions, while mathematical reasoning tasks have remained unexplored due to the dearth of unsolvable math problems. To systematically investigate LLM reliability in mathematical reasoning tasks, we formulate the reliability evaluation for both solvable and unsolvable problems. We then develop a ReliableMath dataset which incorporates open-source solvable problems and high-quality unsolvable problems synthesized by our proposed construction workflow with human evaluations. Experiments are conducted on various LLMs with several key findings uncovered. LLMs fail to directly identify unsolvable problems and always generate fabricated responses. When instructing LLMs to indicate unsolvability using a reliable prompt, the reliability of larger-sized LLMs remains on solvable problems, but notably improves on unsolvable problems yet still falls short of solvable problems. However, small LLMs rarely show any progress despite employing reliable prompts. Therefore, we further propose an alignment strategy to enhance small LLMs' reliability, which can significantly improve LLM reliability performances on both in-domain and out-of-domain tasks.

The Natural Language for Optimization (NL4Opt) Competition was created to investigate methods of extracting the meaning and formulation of an optimization problem based on its text description. Specifically, the goal of the competition is to increase the accessibility and usability of optimization solvers by allowing non-experts to interface with them using natural language. We separate this challenging goal into two sub-tasks: (1) recognize and label the semantic entities that correspond to the components of the optimization problem; (2) generate a meaning representation (i.e., a logical form) of the problem from its detected problem entities. The first task aims to reduce ambiguity by detecting and tagging the entities of the optimization problems. The second task creates an intermediate representation of the linear programming (LP) problem that is converted into a format that can be used by commercial solvers. In this report, we present the LP word problem dataset and shared tasks for the NeurIPS 2022 competition. Furthermore, we investigate and compare the performance of the ChatGPT large language model against the winning solutions. Through this competition, we hope to bring interest towards the development of novel machine learning applications and datasets for optimization modeling.

There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing (NLP) and Image Classification (IC). However, scientific and engineering problems have their own unique characteristics and requirements raising new challenges for effective design and deployment of machine learning approaches. There is a strong need for further mathematical developments on the foundations of machine learning methods to increase the level of rigor of employed methods and to ensure more reliable and interpretable results. Also as reported in the recent literature on state-of-the-art results and indicated by the No Free Lunch Theorems of statistical learning theory incorporating some form of inductive bias and domain knowledge is essential to success. Consequently, even for existing and widely used methods there is a strong need for further mathematical work to facilitate ways to incorporate prior scientific knowledge and related inductive biases into learning frameworks and algorithms. We briefly discuss these topics and discuss some ideas proceeding in this direction.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

The nature of abstract reasoning is a matter of debate. Modern artificial neural network (ANN) models, like large language models, demonstrate impressive success when tested on abstract reasoning problems. However, it has been argued that their success reflects some form of memorization of similar problems (data contamination) rather than a general-purpose abstract reasoning capability. This concern is supported by evidence of brittleness, and the requirement of extensive training. In our study, we explored whether abstract reasoning can be achieved using the toolbox of ANNs, without prior training. Specifically, we studied an ANN model in which the weights of a naive network are optimized during the solution of the problem, using the problem data itself, rather than any prior knowledge. We tested this modeling approach on visual reasoning problems and found that it performs relatively well. Crucially, this success does not rely on memorization of similar problems. We further suggest an explanation of how it works. Finally, as problem solving is performed by changing the ANN weights, we explored the connection between problem solving and the accumulation of knowledge in the ANNs.