arXiv subjects

Mingzhu Wan

Publications and source records attributed to Mingzhu Wan.

3 recordsLinked to original sources

arXiv2026

Deep Divide-and-Reduce in Symbolic Regression

Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions. Building on this paradigm, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a mathematically grounded framework that systematically generalizes expression decomposition and variable reduction. DDRSR extends translational symmetry to coefficient- and exponent-interfered forms, enables variable separation under overlapping variables and additive constant offsets, and generalizes the identification of nested compositional structures. We further characterize an intrinsic non-identifiability limitation of decomposition when no effective variable separation is induced. Experiments across multiple symbolic regression algorithms and benchmark datasets show that DDRSR identifies a broader range of decomposable structures than AI Feynman and overall improves downstream regression accuracy and exact-expression recovery.

cs.LG↗

arXiv2026

ChatSR: Multimodal Large Language Models for Scientific Formula Discovery

Current multimodal large language models (MLLMs) are mainly focused on the understanding and processing of perceptual modalities such as images and videos, while their capability for scientific data understanding remains insufficient. To this end, we propose ChatSR, a novel multimodal large language model tailored for scientific data understanding. ChatSR treats scientific data as a new modality analogous to visual content and, through carefully designed encoders and modality alignment mechanisms, maps scientific data into a representation space that can be processed by large language models, enabling the model to grasp the structural characteristics and underlying regularities of scientific data. Building on this foundation, ChatSR further exploits the rich domain knowledge and strong reasoning abilities of large language models to emulate a knowledgeable human scientist: based on user-specified prior constraints and preferences expressed (such as requirements on periodicity, symmetry, etc.), it automatically generates mathematical formulas that not only accurately fit the observed data but also conform to domain priors, thereby characterizing the latent laws embodied in scientific data and promoting the automation of scientific discovery. Experiments on 13 datasets show that ChatSR achieves state-of-the-art performance on traditional symbolic regression benchmarks. In addition, ChatSR exhibits a promising zero-shot ability to understand and utilize types of prior knowledge that are not present in its training data.

cs.AI↗

arXiv2026

GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing

Mathematical formulas serve as a language through which humans communicate with nature. Discovering mathematical laws from scientific data to describe natural phenomena has been a long-standing pursuit of humanity for centuries. In the field of artificial intelligence, this challenge is known as the symbolic regression problem. Among existing symbolic regression approaches, Genetic Programming (GP) based on evolutionary algorithms remains one of the most classical and widely adopted methods. GP simulates the evolutionary process across generations through genetic mutation and crossover. However, mutations and crossovers in GP are entirely random. While this randomness effectively mimics natural evolution, it inevitably produces both beneficial and detrimental variations. If there existed a metaphorical `God` capable of foreseeing which genetic mutations or crossovers would yield superior outcomes and performing targeted gene editing accordingly, the efficiency of evolution could be substantially improved. Motivated by this idea, we propose in this paper a symbolic regression approach based on gene editing, termed GESR. In GESR, we trained two "hands of God" (two BERT models). Among them, the first leverages the BERT's masked language modeling capability to guide the mutation of genes (expression symbols). The other BERT model guides the crossover of individual genes by predicting the crossover point. Experimental results demonstrate that GESR significantly improves computational efficiency compared with traditional GP algorithms and achieves strong overall performance across multiple symbolic regression tasks.

cs.AI↗