arXiv subjects

Yingfan Hua

Publications and source records attributed to Yingfan Hua.

3 recordsLinked to original sources

arXiv2026

SymbolicLM: Training Language Models as Symbolic Regressors

Large Language Models (LLMs) have shown promising capabilities in scientific reasoning, yet scientific discovery ultimately requires deriving precise laws directly from observational data, known as Symbolic Regression (SR). This poses a challenge for LLMs due to the gap between probabilistic text generation and the exact structural requirements of SR. Existing approaches rely on complex external scaffolds, which are computationally expensive and separate symbolic reasoning from the model itself. To address this limitation, we propose to directly equip LLMs with symbolic regression capabilities through dedicated numerical-symbolic and physical supervision. We introduce PhysSymbArena, a large-scale benchmark containing over 160,000 equations and 1.8B tokens of numerical-symbolic data with physical descriptions, enabling systematic training and evaluation. Based on PhysSymbArena, we develop SymbolicLM, which enhances the symbolic regression ability of LLMs through mathematical and physical supervision. During inference, we further introduce SymbolicSGA, a refinement framework that leverages quantitative feedback to iteratively improve generated equations. Experiments on multiple symbolic regression benchmarks show that SymbolicLM substantially improves structural recovery while maintaining competitive numerical fitting performance. These results demonstrate that symbolic regression can be explicitly learned as an intrinsic capability of LLMs.

cs.CE↗

arXiv2026

Pixel2Phys: Distilling Governing Laws from Visual Dynamics

Discovering physical laws directly from high-dimensional visual data is a long-standing human pursuit but remains a formidable challenge for machines, representing a fundamental goal of scientific intelligence. This task is inherently difficult because physical knowledge is low-dimensional and structured, whereas raw video observations are high-dimensional and redundant, with most pixels carrying little or no physical meaning. Extracting concise, physically relevant variables from such noisy data remains a key obstacle. To address this, we propose Pixel2Phys, a collaborative multi-agent framework adaptable to any Multimodal Large Language Model (MLLM). It emulates human scientific reasoning by employing a structured workflow to extract formalized physical knowledge through iterative hypothesis generation, validation, and refinement. By repeatedly formulating, and refining candidate equations on high-dimensional data, it identifies the most concise representations that best capture the underlying physical evolution. This automated exploration mimics the iterative workflow of human scientists, enabling AI to reveal interpretable governing equations directly from raw observations. Across diverse simulated and real-world physics videos, Pixel2Phys discovers accurate, interpretable governing equations and maintaining stable long-term extrapolation where baselines rapidly diverge.

cs.CE↗

arXiv2025

Finetuning Large Language Model as an Effective Symbolic Regressor

Deriving governing equations from observational data, known as Symbolic Regression (SR), is a cornerstone of scientific discovery. Large Language Models, (LLMs) have shown promise in this task by leveraging their vast cross-disciplinary scientific knowledge. However, existing LLM-based methods primarily rely on direct inference or prompt engineering, often requiring excessive inference iterations to converge on correct formulas or failing to treat complex equation targets. These limitations in effectiveness and generalization stem from an inherent tension between pre-trained LLMs' proficiency in approximate reasoning and the high-precision demands of SR tasks. To bridge this gap, we propose to fine-tune LLMs for enhanced SR capability. Yet, the absence of dedicated datasets for SR-oriented fine-tuning remains a critical barrier. We thus introduce SymbArena, specifically engineered to optimize LLMs for SR. This benchmark comprises over 148,000 diverse equations formulated as corpora of 1.83 billion tokens for LLM utilization, enabling effective training and inference. Further, to ensure a more comprehensive and fair evaluation, SymbArena proposes a heuristics metric to precisely quantify form-level consistency, going beyond existing SR numerical-oriented evaluation strategies. With this benchmark, we explore mainstream LLM fine-tuning techniques for SR tasks and establish Symbolic-R1, a simple yet effective LLM-based SR strong baseline. Experimental results validate Symbolic-R1 as the first LLM to exceed traditional numerical methods in both numerical precision and symbolic form accuracy, outperforming the second-best LLM baseline with improvements of 2-fold gains in R2 score and 10.3% in form-level consistency score.

cs.CE↗