Lei Bai
Publications
Discovery of Interpretable Physical Laws in Materials via Language-Model-Guided Symbolic Regression
Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space of possible forms. We introduce a framework that guides the search process by leveraging the embedded scientific knowledge of large language models, enabling efficient identification of physical laws in the data. We validate our approach by modeling key properties of perovskite materials. Our method mitigates the combinatorial explosion commonly encountered in traditional symbolic regression, reducing the effective search space by a factor of approximately $10^5$. A set of novel formulas for bulk modulus, band gap, and oxygen evolution reaction activity are identified, which not only provide meaningful physical insights but also outperform previous formulas in accuracy and simplicity.
One Brain, Omni Modalities: Towards Unified Non-Invasive Brain Decoding with Large Language Models
Deciphering brain function through non-invasive recordings requires synthesizing complementary high-frequency electromagnetic (EEG/MEG) and low-frequency metabolic (fMRI) signals. However, despite their shared neural origins, extreme discrepancies have traditionally confined these modalities to isolated analysis pipelines, hindering a holistic interpretation of brain activity. To bridge this fragmentation, we introduce \textbf{NOBEL}, a \textbf{n}euro-\textbf{o}mni-modal \textbf{b}rain-\textbf{e}ncoding \textbf{l}arge language model (LLM) that unifies these heterogeneous signals within the LLM's semantic embedding space. Our architecture integrates a unified encoder for EEG and MEG with a novel dual-path strategy for fMRI, aligning non-invasive brain signals and external sensory stimuli into a shared token space, then leverages an LLM as a universal backbone. Extensive evaluations demonstrate that NOBEL serves as a robust generalist across standard single-modal tasks. We also show that the synergistic fusion of electromagnetic and metabolic signals yields higher decoding accuracy than unimodal baselines, validating the complementary nature of multiple neural modalities. Furthermore, NOBEL exhibits strong capabilities in stimulus-aware decoding, effectively interpreting visual semantics from multi-subject fMRI data on the NSD and HAD datasets while uniquely leveraging direct stimulus inputs to verify causal links between sensory signals and neural responses. NOBEL thus takes a step towards unifying non-invasive brain decoding, demonstrating the promising potential of omni-modal brain understanding.
Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision
Large language models (LLMs) have demonstrated exceptional reasoning capabilities, and co-evolving paradigms have shown promising results in domains such as code and math. However, in scientific reasoning tasks, these models remain fragile due to unreliable solution evaluation and limited diversity in verification strategies. In this work, we propose Sci-CoE, a two-stage scientific co-evolving framework that enables models to self-evolve as both solver and verifier through a transition from sparse supervision to unsupervised learning. In the first stage, the model uses a small set of annotated data to establish fundamental correctness judgment anchors for the Verifier. In the second stage, we introduce a geometric reward mechanism that jointly considers consensus, reliability, and diversity, driving large-scale self-iteration on unlabeled data. Experiments on several general scientific benchmarks demonstrate that Sci-CoE enhances complex reasoning capabilities and exhibits strong scalability, facilitating the construction of more robust and diverse evaluation systems. Codes are available at https://github.com/InternScience/Sci-CoE.