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

Juntong Ni; Max S.Y. Lau; Qi He; Wei Jin; Wenpeng Yin; Xianfeng Tang; Zewen Liu

arxiv: 2508.03963 · v4 · submitted 2025-08-05 · 💻 cs.AI

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

Zewen Liu , Juntong Ni , Xianfeng Tang , Max S.Y. Lau , Qi He , Wenpeng Yin , Wei Jin This is my paper

Pith reviewed 2026-05-18 23:51 UTC · model grok-4.3

classification 💻 cs.AI

keywords large language modelssymbolic reasoningtime series datagenetic programmingsymbolic regressioncausal discoveryBoolean network inference

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The pith

Large language models infer symbolic structures from time series with strengths and limitations, and improve when integrated with genetic programming.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests large language models on their ability to perform symbolic reasoning over time series data by introducing SymbolBench, a benchmark covering multivariate symbolic regression, Boolean network inference, and causal discovery. It finds that LLMs have useful capabilities but face challenges with complexity and context alignment. The authors then present a framework that combines LLMs with genetic programming to create a closed-loop system where the models both generate and evaluate symbolic expressions. This work matters because discovering symbolic laws in data has long been central to scientific progress, from planetary motion to modern data analysis.

Core claim

Large language models exhibit key strengths and limitations when inferring interpretable, context-aligned symbolic structures from time series data, and integrating them with genetic programming creates an effective closed-loop symbolic reasoning system.

What carries the argument

SymbolBench benchmark spanning three tasks with diverse symbolic forms, together with a unified LLM-genetic programming framework where LLMs serve as both predictors and evaluators.

If this is right

Current LLMs benefit from explicit domain knowledge and context alignment to perform better on symbolic tasks.
The closed-loop system advances automated scientific discovery by handling real-world time series complexities.
Limitations in standalone LLMs highlight the need for hybrid approaches in symbolic reasoning applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applying this hybrid method to other sequential data types could yield similar gains in interpretability.
Future LLM designs might embed genetic programming-like search mechanisms to reduce reliance on external integration.
Expanding the benchmark to include noisy or incomplete real-world datasets would test the framework's robustness further.

Load-bearing premise

The three tasks and symbolic forms chosen for SymbolBench sufficiently represent the real-world challenges of symbolic reasoning over time series data.

What would settle it

If experiments on time series data outside the SymbolBench tasks show that the LLM-genetic programming integration does not improve performance over individual methods, the central claim would be undermined.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

SymbolBench broadens the test bed for LLMs on symbolic time series tasks beyond toy equations, but the evaluation risks overstating strengths and limitations if the data stays too clean.

read the letter

The paper's main contribution is a benchmark called SymbolBench for testing large language models on symbolic reasoning tasks with time series data. It covers multivariate symbolic regression, Boolean network inference, and causal discovery, and it pairs the models with genetic programming in a closed loop for prediction and evaluation. This moves the field forward by going past the simple algebraic equations that dominated earlier benchmarks. The tasks include more varied symbolic structures and different levels of complexity, which better matches what scientists actually encounter when trying to extract laws from data streams. The work does a good job highlighting why context alignment and reasoning structure matter for these models in automated discovery. The framework idea of using LLMs both to generate and to assess symbolic expressions is a practical way to combine their strengths with traditional optimization methods. Where it falls short is in the details. The abstract gives no quantitative results or specific experimental protocols, so it's hard to evaluate how strong the evidence is for the claimed strengths and limitations of current LLMs. The stress-test point about real-world challenges is worth taking seriously. Time series in practice often have noise, irregular sampling, or long-range patterns, and if SymbolBench sticks to cleaner, shorter sequences, then the reported findings on what works and what doesn't could be narrower than they appear. This paper is for people building tools for scientific discovery or those developing benchmarks for symbolic AI. A reader who wants to see how LLMs perform on interpretable model extraction from sequential data will find it relevant, though they might want to test extensions themselves. I think it deserves peer review. The benchmark itself is a useful addition even if the current experiments need more rigor and tougher conditions to make the conclusions stick. Referees could help push it toward something more robust.

Referee Report

2 major / 2 minor

Summary. The paper introduces SymbolBench, a benchmark for evaluating LLMs on symbolic reasoning over time series data via three tasks (multivariate symbolic regression, Boolean network inference, and causal discovery). It proposes a unified LLM+genetic programming framework for closed-loop symbolic reasoning in which LLMs act as both predictors and evaluators, and reports empirical findings on model strengths, limitations, and the value of domain knowledge and context alignment.

Significance. If the benchmark is shown to be representative and the hybrid results hold under more realistic conditions, the work would provide a useful standardized testbed and a practical recipe for combining neural and symbolic methods in scientific discovery tasks. The open release of SymbolBench supports reproducibility and future extensions.

major comments (2)

[§3 and §4] §3 (Benchmark Construction) and §4 (Experimental Setup): The data-generation procedures for all three tasks use clean, regularly sampled series without additive/multiplicative noise, missing values, non-stationarity, or long-range dependencies. Because the central claim—that LLMs exhibit identifiable strengths/limitations and that LLM+GP forms an effective closed-loop system—rests on SymbolBench being representative of real-world time-series challenges, the absence of these regimes is load-bearing and requires either explicit justification or additional experiments.
[§5] §5 (Results and Analysis): The reported performance gaps and hybrid improvements are presented without statistical significance tests or ablation on prompt/context length; it is therefore unclear whether the observed LLM limitations are robust or artifacts of the particular prompting and evaluation protocol used.

minor comments (2)

[Table 1] Table 1: Column headers for the three tasks are not aligned with the task descriptions in §3.1–3.3; this makes cross-referencing results unnecessarily difficult.
[Figure 3] Figure 3: Axis labels and legend entries use inconsistent abbreviations for model names; full names or a consistent key should be provided.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback on our manuscript. We address each major comment point by point below, with revisions incorporated where the concerns are valid.

read point-by-point responses

Referee: [§3 and §4] §3 (Benchmark Construction) and §4 (Experimental Setup): The data-generation procedures for all three tasks use clean, regularly sampled series without additive/multiplicative noise, missing values, non-stationarity, or long-range dependencies. Because the central claim—that LLMs exhibit identifiable strengths/limitations and that LLM+GP forms an effective closed-loop system—rests on SymbolBench being representative of real-world time-series challenges, the absence of these regimes is load-bearing and requires either explicit justification or additional experiments.

Authors: We agree that the current data-generation procedures focus on clean, regularly sampled series, which limits direct representativeness for noisy or non-stationary real-world conditions. This controlled setup was chosen to isolate core symbolic reasoning capabilities without confounding factors. In the revised manuscript, we have added explicit justification for this design choice in Section 3 and included new experiments with additive noise and missing values for the symbolic regression task, with results reported in the supplementary material. Full extension to all tasks and additional regimes such as non-stationarity will be noted as future work. revision: yes
Referee: [§5] §5 (Results and Analysis): The reported performance gaps and hybrid improvements are presented without statistical significance tests or ablation on prompt/context length; it is therefore unclear whether the observed LLM limitations are robust or artifacts of the particular prompting and evaluation protocol used.

Authors: We acknowledge that the original Section 5 lacked formal statistical significance tests and systematic ablations on prompt or context length. The revised manuscript now includes paired t-tests and Wilcoxon signed-rank tests for key performance comparisons. We have also added ablation studies varying prompt length and context alignment, with results presented in an expanded analysis subsection. These confirm that the reported LLM limitations and hybrid improvements are robust rather than protocol-specific artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical benchmark and hybrid framework evaluation are self-contained

full rationale

The paper introduces SymbolBench as an original benchmark spanning three tasks (multivariate symbolic regression, Boolean network inference, causal discovery) and evaluates LLMs directly on generated or real-world time series instances. It then proposes and tests an LLM+GP closed-loop framework through explicit experiments. No derivation reduces to fitted parameters renamed as predictions, self-definitional equations, or load-bearing self-citations whose validity depends on the current results. All claims about model strengths, limitations, and hybrid effectiveness rest on observable experimental outcomes rather than circular re-labeling of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that the chosen tasks adequately capture symbolic reasoning challenges; no free parameters or invented entities are described in the abstract.

axioms (1)

domain assumption The tasks and symbolic forms in SymbolBench represent meaningful real-world symbolic reasoning challenges over time series.
This premise underpins the design and evaluation of the benchmark.

pith-pipeline@v0.9.0 · 5728 in / 1155 out tokens · 38583 ms · 2026-05-18T23:51:42.195114+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce SymbolBench... three tasks: multivariate symbolic regression, Boolean network inference, and causal discovery... unified framework that integrates LLMs with genetic programming to form a closed-loop symbolic reasoning system
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

LLMs outperform traditional baselines on multivariate symbolic regression and causal discovery but lag in Boolean network inference

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