arXiv subjects

Leheng Chen

Publications and source records attributed to Leheng Chen.

9 recordsLinked to original sources

arXiv2026

Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.

cs.AI↗

arXiv2026

Iteris: Agentic Research Loops for Computational Mathematics

Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.

cs.AI↗

arXiv2026

Matlas: A Semantic Search Engine for Mathematics

Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics, where reliable grounding is essential. However, the scale and structure of the mathematical literature pose significant challenges: results are distributed across millions of documents, and individual statements are often difficult to interpret in isolation due to their dependence on prior definitions and theorems. In this paper, we introduce Matlas, a semantic search engine for mathematical statements. Matlas is built on a large-scale corpus of 8.07 million statements extracted from 435K peer-reviewed papers spanning 1826 to 2025, drawn from a curated set of 180 journals selected using an ICM citation-based criterion, together with 1.9K textbooks. From these sources, we extract mathematical statements together with their dependencies, construct document-level dependency graphs, and recursively unfold statements in topological order to produce more self-contained representations. On top of this corpus, we develop a semantic retrieval system that enables efficient search for mathematical results using natural language queries. We hope that Matlas can improve the efficiency of theorem retrieval for mathematicians and provide a structured source of grounding for AI systems tackling research-level mathematical problems, and serve as part of the infrastructure for mathematical knowledge retrieval.

cs.IR↗

arXiv2026

Automated Conjecture Resolution with Formal Verification

Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework that integrates natural language reasoning with formal verification to tackle research-level mathematical problems. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas combines reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with LeanSearch, translates informal arguments into formalized Lean 4 projects through task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Additional case studies illustrate the capabilities of Rethlas in informal mathematical reasoning and discovery, as well as the ability of Archon to formalize research-level proofs in Lean 4. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent can autonomously fill nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, reduce human effort, and support human-AI collaborative mathematical research.

cs.LG↗

arXiv2025

SciAgent: A Unified Multi-Agent System for Generalistic Scientific Reasoning

Recent advances in large language models have enabled AI systems to achieve expert-level performance on domain-specific scientific tasks, yet these systems remain narrow and handcrafted. We introduce SciAgent, a unified multi-agent system designed for generalistic scientific reasoning-the ability to adapt reasoning strategies across disciplines and difficulty levels. SciAgent organizes problem solving as a hierarchical process: a Coordinator Agent interprets each problem's domain and complexity, dynamically orchestrating specialized Worker Systems, each composed of interacting reasoning Sub-agents for symbolic deduction, conceptual modeling, numerical computation, and verification. These agents collaboratively assemble and refine reasoning pipelines tailored to each task. Across mathematics and physics Olympiads (IMO, IMC, IPhO, CPhO), SciAgent consistently attains or surpasses human gold-medalist performance, demonstrating both domain generality and reasoning adaptability. Additionally, SciAgent has been tested on the International Chemistry Olympiad (IChO) and selected problems from the Humanity's Last Exam (HLE) benchmark, further confirming the system's ability to generalize across diverse scientific domains. This work establishes SciAgent as a concrete step toward generalistic scientific intelligence-AI systems capable of coherent, cross-disciplinary reasoning at expert levels.

cs.AI↗

arXiv2025

PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with adequate accuracy, and limitations of the traditional solvers and specialized neural operators motivate the development of foundation models for solving PDEs. This paper introduces PDEformer-2, a versatile foundation model for two-dimensional PDEs. Based on our previous one-dimensional PDEformer-1 model, PDEformer-2 receives the PDE form as network input via computational graph representation, which has the flexibility to encode most common PDEs. The mesh-free predicted solutions can be directly queried at arbitrary spatio-temporal coordinates. A large (40TB) diverse dataset is employed to pretrain the current model, making it capable of simultaneously addressing PDEs with different symbolic forms, domain shapes, boundary conditions, number of variables, and time-dependency. Accurate zero-shot prediction is allowed for PDEs that resemble the pretraining ones. When adapted to new unseen PDEs, PDEformer-2 demonstrates faster learning than many specialized models, and has smaller errors given limited (less than 100) samples. Additionally, PDEformer-2 can be employed in the inverse problems thanks to its fast and differentiable nature and produces reasonable results in our experiments to recover coefficient scalars and fields of a PDE.

math.NA↗

arXiv2025

PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that is comparable to those of specifically trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery.

math.NA↗

arXiv2025

PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations

This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of symbolic and numeric information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed subsequently to generate mesh-free predicted solutions. We generated a dataset with up to three million samples involving diverse one-dimensional PDEs to pretrain our model. Compared with baseline models trained specifically on benchmark datasets, our pretrained model achieves comparable accuracy via zero-shot inference, and the advantage expands after finetuning. For PDEs new or unseen in the pretraining stage, our model can adapt quickly by finetuning on a relatively small set of examples from the target equation. Additionally, PDEformer-1 demonstrates promising results in the inverse problem of PDE scalar coefficient recovery and coefficient field recovery.

math.NA↗

arXiv2024

Modeling Heat Conduction with Dual-Dissipative Variables: A Mechanism-Data Fusion Method

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite or other small perturbation expansion methods. These macroscopic models have made great success on capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly non-equilibrium or ballistic thermal transport. In this paper, we provide a new strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep learning methods combined with non-equilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of Conservation-Dissipation Formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine-tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.

physics.comp-ph↗