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arxiv: 2606.12481 · v1 · pith:C7JZVH42new · submitted 2026-06-10 · 💻 cs.LG · cs.AI

Representing Time Series as Structured Programs for LLM Reasoning

Jaeho Kim , Changhun Oh , Seokhyun Lee , Irina Rish , Changhee Lee This is my paper

Pith reviewed 2026-06-27 11:03 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords time serieslarge language modelsstructured programstemporal decompositionLLM reasoningtraining-free methodtime series analysis
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The pith

Converting time series into structured symbolic programs lets off-the-shelf LLMs reason about them without fine-tuning or raw serialization.

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

The paper proposes T2SP, a method that turns time series data into structured programs describing trends, periods, and salient events. This moves the work of finding temporal patterns out of the LLM and into the input format itself. As a result, standard LLMs perform better on editing, captioning, and question-answering tasks involving time series, while using less time and failing less often. The approach is training-free and deterministic, aligning the data with the textual and code modalities LLMs already handle well.

Core claim

T2SP is 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.

What carries the argument

T2SP representation, which decomposes any time series into trends, periods, and salient events expressed as a structured symbolic program.

If this is right

  • Performance improves on time-series editing, captioning, and question answering compared with raw-string inputs.
  • Reasoning time decreases for these tasks.
  • Failure rates drop when LLMs receive the structured program format.
  • Off-the-shelf LLMs can be applied directly without fine-tuning on time-series data.

Where Pith is reading between the lines

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

  • The same pre-structuring idea could be tested on other non-text data such as images or audio by converting them into symbolic descriptions first.
  • Because the output is a readable program, humans might inspect or edit the temporal decomposition before feeding it to the LLM.
  • Longer sequences might show even larger gains since raw serialization tends to degrade more sharply with length.

Load-bearing premise

A deterministic decomposition of any time series into trends, periods, and salient events can be expressed in a program-friendly format that reliably aligns with LLM textual and code-like modalities without introducing errors.

What would settle it

A counterexample where the T2SP program for a given time series causes an LLM to produce incorrect outputs on editing, captioning, or question-answering tasks while the raw numerical string succeeds.

Figures

Figures reproduced from arXiv: 2606.12481 by Changhee Lee, Changhun Oh, Irina Rish, Jaeho Kim, Seokhyun Lee.

Figure 1
Figure 1. Figure 1: Representations matter for LLM-based time￾series reasoning. (A) Raw numerical sequences are dense and heterogeneous, forcing LLMs to infer the temporal structure value by value. (B) LLMs are pretrained on a vast corpus of natural language texts and code representations (Touvron et al., 2023), making them well-suited for reasoning over symbolic and functional forms (Gao et al., 2023; Chen et al., 2023). 202… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of T2SP. A time series is decomposed into structured components – trend, periods, and events – through a sequential pipeline. Each component, together with its parameters, is expressed as a symbolic abstract representation of the time series. This program-friendly representation, along with a natural language description of each component and an instruction q, is then passed to an LLM for downstre… view at source ↗
Figure 3
Figure 3. Figure 3: Time Taken and Success Rate Across Sequence Length. The left and right axes represent the time taken (seconds) to perform the editing and the success rate, respec￾tively. The three representations perform comparably up to a sequence length of 256, beyond which the raw and vision￾based baselines deteriorate rapidly, while T2SP remains stable. required output format. In addition to the LLM￾based methods, we … view at source ↗
Figure 4
Figure 4. Figure 4: Example of T2SP representation. We format the trend, events, and periods into a structured symbolic abstract representation. This representation is human-interpretable and invertible [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Decomposition from T2SP. We provide a visual illustration of the decomposition. B Datasets & Baseline Implementation B.1 TSEdit Dataset We construct the TSEdit dataset to evaluate instruction-based time-series editing. Prior work on time-series editing (Qiu et al., 2026) adopts an attribute-based formulation, where edits are framed as adding or removing the presence of a predefined attribute in the series … view at source ↗
Figure 6
Figure 6. Figure 6: Streamlit-based Annotation Framework. We capture the annotation interface used in our experiment. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Editing results on ETTh1 task. The grey and red lines show the original and edited time series, respectively. T2SP produces precise, component-level edits across trend, periodicity, and event instructions, while Raw and Vision baselines often fail to localize changes or even corrupt unrelated structure. N-shot Method Gemini-3.1-flash-lite Claude-haiku-4.5 Wafer ECG200 Wafer ECG200 Acc ↑ F1 ↑ Acc ↑ F1 ↑ Acc… view at source ↗
Figure 8
Figure 8. Figure 8: Captioning results. E Prompts Listing 1: Prompt for Editing Task (TSEdit-Trend) ========================================= Sample ID : trend_L32_0000 Category : trend Edit type : edit_flatten Instruction: Flatten the trend to be constant over time. ========================================= You are a time-series program editing expert. Your task is to modify the symbolic program that represents a time series… view at source ↗
read the original abstract

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.

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.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces T2SP, a deterministic, training-free method that represents time series as structured symbolic programs by decomposing them into trends, periods, and salient events expressed in a program-friendly format. This is claimed to shift temporal structure extraction away from the LLM, enabling off-the-shelf models to achieve better performance on editing, captioning, and question-answering tasks while reducing reasoning time and failure rates relative to raw-string representations.

Significance. If the results hold, T2SP could provide a practical, parameter-free interface for applying LLMs to time-series reasoning without fine-tuning or modality mismatch. The deterministic and training-free design is a clear strength, avoiding circularity or learned parameters and directly leveraging LLMs' existing code and text capabilities. This has potential implications for efficient temporal analysis in domains where labeled time-series data is scarce.

major comments (2)
  1. [Abstract] Abstract: the claim that T2SP 'consistently improves performance' on the three tasks is presented without quantitative results, baselines, error bars, dataset details, or description of how the decomposition is performed, so the data-to-claim link cannot be evaluated.
  2. [T2SP method description] T2SP method description: no quantitative fidelity metric (e.g., reconstruction error or alignment with ground-truth structure) or failure-case analysis is supplied for the deterministic decomposition into trends/periods/events. This is load-bearing for the central premise that the representation introduces no errors that could degrade LLM reasoning on complex or noisy series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments correctly identify opportunities to strengthen the abstract's self-containment and to provide explicit validation of the decomposition step. We address each major comment below and commit to revisions that directly respond to the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that T2SP 'consistently improves performance' on the three tasks is presented without quantitative results, baselines, error bars, dataset details, or description of how the decomposition is performed, so the data-to-claim link cannot be evaluated.

    Authors: We agree that the abstract, being a concise summary, does not embed the supporting quantitative details. The body of the manuscript (Sections 4 and 5) reports the full results, including baselines, error bars, dataset descriptions, and per-task metrics that substantiate the 'consistently improves' claim. To improve self-containment, we will revise the abstract to incorporate brief quantitative highlights (e.g., average relative gains) and a short clause describing the deterministic decomposition into trends, periods, and events. revision: yes

  2. Referee: [T2SP method description] T2SP method description: no quantitative fidelity metric (e.g., reconstruction error or alignment with ground-truth structure) or failure-case analysis is supplied for the deterministic decomposition into trends/periods/events. This is load-bearing for the central premise that the representation introduces no errors that could degrade LLM reasoning on complex or noisy series.

    Authors: The decomposition employs standard, deterministic signal-processing routines whose fidelity is implicit in their design. Nevertheless, we accept that an explicit quantitative check would strengthen the central premise. In the revised manuscript we will add a dedicated fidelity subsection reporting reconstruction error (MSE between original and program-reconstructed series) across the evaluation datasets together with a brief analysis of failure modes on noisy or irregular inputs. revision: yes

Circularity Check

0 steps flagged

No circularity: deterministic representation method with external baselines

full rationale

The paper introduces T2SP as a deterministic, training-free decomposition of time series into trends/periods/events expressed in program format. No equations, fitted parameters, or predictions are defined in terms of themselves. Performance is measured against raw-string baselines on editing/captioning/QA tasks, providing independent empirical content. No self-citation chains or uniqueness theorems are invoked as load-bearing premises in the provided text. The central claim reduces to the method's design and measured gains rather than any definitional loop or renamed input.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that time series admit a useful decomposition into trends, periods, and salient events that can be rendered symbolically; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Time series data can be decomposed into trends, periods, and salient events in a way that produces a program-friendly symbolic representation aligned with LLM training modalities.
    This decomposition is the core mechanism that shifts structure extraction away from the LLM; it is invoked when the abstract describes T2SP as expressing the series in program format.

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discussion (0)

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Reference graph

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