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

arXiv: https://arxiv.org/abs/2508.03963 · HTML: https://mlsanity.com/paper/2508.03963/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Time series reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- LLM reasoning / [Time series reasoning](https://mlsanity.com/lr/time-series-reasoning/)

## Builds on (most cited first, 20 of 20)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [Exploring the Reasoning Abilities of Multimodal Large Language Models (MLLMs): A Comprehensive Survey on Emerging Trends in Multimodal Reasoning](https://mlsanity.com/paper/2401.06805/) (2024)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [ChatTS: Aligning Time Series with LLMs via Synthetic Data for Enhanced Understanding and Reasoning](https://mlsanity.com/paper/2412.03104/) (2024)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [LLM Reasoners: New Evaluation, Library, and Analysis of Step-by-Step Reasoning with Large Language Models](https://mlsanity.com/paper/2404.05221/) (2024)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Reasoning Language Models: A Blueprint](https://mlsanity.com/paper/2501.11223/) (2025)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [KERAP: A Knowledge-Enhanced Reasoning Approach for Accurate Zero-shot Diagnosis Prediction Using Multi-agent LLMs](https://mlsanity.com/paper/2507.02773/) (2025)
- [TempoGPT: Enhancing Time Series Reasoning via Quantizing Embedding](https://mlsanity.com/paper/2501.07335/) (2025)
- [ChatSR: Multimodal Large Language Models for Scientific Formula Discovery](https://mlsanity.com/paper/2406.05410/) (2024)
- [LLM-ABBA: Understanding time series via symbolic approximation](https://mlsanity.com/paper/2411.18506/) (2024)

## Built on by (most cited first, 6 of 6)

- [A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models](https://mlsanity.com/paper/2509.11575/) (2025)
- [LUNE: Efficient LLM Unlearning via LoRA Fine-Tuning with Negative Examples](https://mlsanity.com/paper/2512.07375/) (2025)
- [STReasoner: Empowering LLMs for Spatio-Temporal Reasoning in Time Series via Spatial-Aware Reinforcement Learning](https://mlsanity.com/paper/2601.03248/) (2026)
- [PPG-Distill: Efficient Photoplethysmography Signals Analysis via Foundation Model Distillation](https://mlsanity.com/paper/2509.19215/) (2025)
- [Adaptive Time Series Reasoning via Segment Selection](https://mlsanity.com/paper/2602.18645/) (2026)
- [MATRIX: A Multimodal Benchmark and Post-Training Framework for Materials Science](https://mlsanity.com/paper/2602.00376/) (2026)

## Abstract (arXiv)

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.