# Representing Time Series as Structured Programs for LLM Reasoning

arXiv: https://arxiv.org/abs/2606.12481 · HTML: https://mlsanity.com/paper/2606.12481/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Time series reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [OpenTSLM: Time-Series Language Models for Reasoning over Multivariate Medical Text- and Time-Series Data](https://mlsanity.com/paper/2510.02410/) (2025)
- [Harnessing Vision Models for Time Series Analysis: A Survey](https://mlsanity.com/paper/2502.08869/) (2025)
- [FoNE: Precise Single-Token Number Embeddings via Fourier Features](https://mlsanity.com/paper/2502.09741/) (2025)
- [BEDTime: A Unified Benchmark for Automatically Describing Time Series](https://mlsanity.com/paper/2509.05215/) (2025)
- [Adaptive Time Series Reasoning via Segment Selection](https://mlsanity.com/paper/2602.18645/) (2026)
- [LLaTiSA: Towards Difficulty-Stratified Time Series Reasoning from Visual Perception to Semantics](https://mlsanity.com/paper/2604.17295/) (2026)

## Built on by (most cited first, 2 of 2)

- [T-SMART: Mechanism-Level Attribution for Tool-Augmented Time-Series Question Answering](https://mlsanity.com/paper/2609.14142/) (2026)
- [TimeNet: An Extensible Unified Data Infrastructure for Next-Generation Temporal Foundation Models](https://mlsanity.com/paper/2610.04407/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated strong reasoning and instruction-following capabilities, making them potentially powerful tools for time-series analysis. However, time series lie outside their native textual modality, raising a fundamental question: how should time series be represented so that LLMs can reason about them effectively? Existing work typically serializes raw numerical sequences or fine-tunes pre-trained LLMs on time-series data. These approaches place the burden of extracting temporal structure directly on the LLM, creating a modality mismatch that often degrades performance on long sequences and introduces substantial computational overhead. In this work, we introduce Time-Series-to-Structured-Program representation (T2SP), a deterministic, training-free method that represents a time series as a structured symbolic program. T2SP decomposes time series into trends, periods, and salient events, expressing them in a program-friendly format aligned with the textual and code-like modalities on which LLMs are natively trained. By shifting temporal-structure extraction from the model to the representation itself, T2SP enables off-the-shelf LLMs to leverage their existing reasoning capabilities for time-series understanding. We evaluate T2SP on three reasoning tasks -- editing, captioning, and question answering -- where it consistently improves performance, reduces reasoning time, and lowers failure rates compared with raw-string representations. Our results demonstrate that T2SP provides an effective interface between time series and LLMs.