Can Large Language Models Adequately Perform Symbolic Reasoning Over Time Series?

TL;DR

This paper introduces SymbolBench, a benchmark for evaluating large language models' ability to perform symbolic reasoning over time series data, and proposes a hybrid framework combining LLMs with genetic programming.

Contribution

The paper presents a new benchmark, SymbolBench, for assessing symbolic reasoning in time series, and a unified LLM-genetic programming framework for scientific discovery.

Findings

LLMs show strengths in certain symbolic tasks but have notable limitations.

Combining domain knowledge with LLMs improves reasoning performance.

The hybrid framework outperforms standalone models in symbolic inference.

Abstract

Uncovering hidden symbolic laws from time series data, as an aspiration dating back to Kepler's discovery of planetary motion, remains a core challenge in scientific discovery and artificial intelligence. While Large Language Models show promise in structured reasoning tasks, their ability to infer interpretable, context-aligned symbolic structures from time series data is still underexplored. To systematically evaluate this capability, we introduce SymbolBench, a comprehensive benchmark designed to assess symbolic reasoning over real-world time series across three tasks: multivariate symbolic regression, Boolean network inference, and causal discovery. Unlike prior efforts limited to simple algebraic equations, SymbolBench spans a diverse set of symbolic forms with varying complexity. We further propose a unified framework that integrates LLMs with genetic programming to form a closed-loop symbolic reasoning system, where LLMs act both as predictors and evaluators. Our empirical results reveal key strengths and limitations of current models, highlighting the importance of combining domain knowledge, context alignment, and reasoning structure to improve LLMs in automated scientific discovery. https://github.com/nuuuh/SymbolBench.