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REVIEW 4 major objections 5 minor 1 cited by

TOKON: TOKenization-Optimized Normalization for time series analysis with a large language model

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper claims that representing every time-series value as a single integer token in the tokenizer's dictionary reduces the tokenized sequence by two to three times and improves multi-step forecasting RMSE by roughly 7-18 percent (up…

desk verdict The TOKON idea—map time series values to integer tokens—is cheap, concrete, and new, but the paper as written overclaims: the single-token premise is unverified, the evaluation lacks standard normalization baselines and error bars, and the parameter search may be circular. read the letter →

arxiv 2502.05701 v1 pith:ALZM2WUE submitted 2025-02-08 cs.LG

Janghoon Yang This is my paper · ORCID
classification cs.LG
keywords TOKONtokenization-optimizednormalizationtimeseriesforecastinglargelanguagemodelszero-shotpromptingtokenizerdictionaryTSFCprompt
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes TOKON, a normalization that rounds each time-series value to an integer inside the tokenizer's dictionary so that every value becomes exactly one token. On two univariate datasets used with a commercial LLM, it reports multi-step forecasting error reductions of roughly 7 percent to 18 percent in RMSE relative to unnormalized prompts, with the largest gain about 28 percent on one dataset. A companion prompt, Time Series Forecasting with Care (TSFC), asks the model to analyze trends and seasonality rather than decompose the series, and yields further improvements on one dataset while stabilizing worst-step errors on both. The paper argues that these gains come without fine-tuning, extra modules, or tokenizer modifications.

What carries the argument

The central object is the tokenizer's dictionary of integers: the paper assumes the dictionary contains every integer from 0 to 999 as a single token. TOKON maps each series value into that dictionary through $v_{i,j} = \max(\min(r(\sigma_T (s_{i,j}-m_s)/\sigma_s + m_T), I_{\max}), I_{\min})$, fixing $m_T$ at the middle of the integer range and choosing $\sigma_T$ by a golden-section one-dimensional search that minimizes forecast cost on a 100-sample subset. The TSFC prompt supplies the second mechanism: instead of asking for decomposition, it instructs the model to identify and use trends and seasonality and to execute algebraic operations carefully, targeting failure modes observed when LLMs handle multiple operations and long-term patterns.

What would settle it

Run each decimal integer from 0 to 999 through the exact tokenizer used in the experiments and count the output tokens; if any integer is produced as more than one token, TOKON's claimed reduction in token count and its simplification argument do not hold.

Watch

Extended reading notes

Core claim

The central claim is that the fragmentation of floating-point numbers by LLM tokenizers is a correctable representational weakness, and normalizing every value to a single dictionary integer removes it. TOKON standardizes the series with dataset-level mean and standard deviation, scales to a target mean and standard deviation, rounds to the nearest integer, and clips to the tokenizer's integer range, preserving ordinal information while making each element one token. Under this representation the tokenized sequence shortens by a factor of two or three and the original per-value forecasting task remains intact. Across baseline, chain-of-thought, and the proposed TSFC prompts, the paper reports consistent RMSE and MAE improvements, with TSFC giving the best or near-best per-step performance.

Load-bearing premise

The load-bearing premise is that the tokenizer really does encode every integer from 0 to 999 as a single token; the paper states this but offers no tokenization check, and if any integer splits into multiple tokens the token-count reduction and the simplification argument do not follow.

Editorial extensions

If this is right

  • Every series value costs exactly one token, so prompts shrink by two to three times and API costs for long-horizon forecasts drop accordingly.
  • The error reductions are reported across baseline, chain-of-thought, and TSFC prompts, so the gain is tied to the normalization rather than to a single prompting style.
  • Combining TOKON with TSFC reduces RMSE further on the household electricity dataset and gives the smallest worst per-step error on both datasets.
  • Because no fine-tuning or adapters are used, the method can be applied to a frozen LLM with only a pre-processing step and a prompt change.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the contiguous integer-dictionary property holds for other LLMs, TOKON should transfer to them as-is; a quick tokenizer audit would identify which models qualify.
  • The reported gain may mix two effects—removing multi-token number fragmentation and shifting the numeric scale—so an ablation that rounds but does not rescale could separate them.
  • The dataset-level one-dimensional search suggests a cheap per-series or per-variable extension for multivariate series, though the paper does not test that and scale heterogeneity across variables remains open.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes TOKON, a normalization method that maps each time series value to an integer token in an LLM tokenizer's dictionary, with parameters m_T and sigma_T set by a 1D golden-section search on the first 100 samples of each dataset. It also introduces a prompt called TSFC (also written TFSC) that asks the LLM to analyze trends and seasonality while performing algebraic operations carefully. Experiments with GPT-4o-mini on two datasets (AIHEPC and a subset of M4) report RMSE/MAE improvements from TOKON of roughly 7% to 18% (and up to 27.83% on SM4), along with a claimed 2-3x reduction in token count. The paper positions TOKON as a zero-shot, fine-tuning-free way to improve LLM time-series forecasting.

Significance. If the central claims hold, the paper offers a simple, broadly applicable normalization technique that improves zero-shot LLM forecasting without additional modules or fine-tuning, and a prompt that helps in some settings. The idea of aligning normalization with tokenizer vocabulary is interesting and potentially useful. However, the manuscript currently does not verify the load-bearing tokenizer assumption, does not describe a clear train/test split for the parameter search, and lacks standard normalization baselines and repeated-run statistics. These omissions make the reported improvements not yet convincing, although the claims are testable and the approach is worth further investigation.

major comments (4)
  1. [Section IV, Parameterization with 1D Search] The parameter sigma_T is selected by minimizing RMSE on the first 100 samples of each dataset using the golden-section search in Figure 1, but no explicit test split is described. The paper reports improvements on the dataset without clarifying whether those 100 samples are excluded from the reported RMSE values. As written, the reported gains may be in-sample fitted values rather than out-of-sample predictions. Please specify the exact data split, confirm that the first 100 samples are held out from evaluation, and report results on a disjoint test set.
  2. [Section III.A and Section IV, Models and Tokenizers] The core premise that GPT-4o-mini's Tiktoken BPE dictionary contains all integers from 0 to 999 as single tokens is asserted but never verified. TOKON's claimed benefit of one token per value and a 2-3x token reduction depends entirely on this property; if some integers split into multiple tokens, the simplification argument and the reported improvements are not supported. Please provide a direct tokenizer verification, such as a list or count of single-token integers in the range 0-999, and token-count comparisons on actual prompts with and without TOKON.
  3. [Tables I-III and Section IV, Main Results] No standard normalization baselines are included. The paper compares TOKON only against the unnormalized case, so the observed improvements could be due to any normalization rather than to the tokenization-aware design. Please add baselines with z-score, min-max, and instance normalization under identical prompts, and report multiple runs with variance or significance tests, since the tables contain single-point estimates.
  4. [Section III.B and Eq. (1)] The assumption that numeric values are symmetrically distributed, which justifies fixing m_T to the interval midpoint, is stated without supporting evidence. For skewed or asymmetric series, this choice could systematically bias the normalized values. Please either validate the symmetry assumption on the datasets used or treat m_T as an additional search parameter in a sensitivity analysis.
minor comments (5)
  1. [Abstract and Introduction] The acronym for the proposed prompt is written as both TFSC and TSFC in different places; please use one consistent spelling throughout.
  2. [Table III] The table caption appears duplicated ('PERFORMANCE WITH PERFORMANCE WITH SM4 DATASET') and should be corrected.
  3. [Section IV, Datasets] The dataset description would benefit from more detail: the construction of the SM4 subset, the forecast horizons for each series length, and how train/test splits were made are not fully specified.
  4. [References] Reference [20] is described as 'submitted' rather than published or arXiv-available; please provide a citable source or remove reliance on it for claims about LLM behavior.
  5. [Section III.A, Eq. (1)] The notation in Eq. (1) is difficult to read because of OCR-style artifacts; please use clean mathematical notation and define r(.), I_min, I_max, and the sample statistics clearly.

Circularity Check

0 steps flagged · score 0.0 of 10

No demonstrated circularity: reported gains are empirical and the token-count claim derives from an explicit, if unverified, dictionary assumption.

full rationale

Walking the derivation chain, TOKON's Eq. (1) is an affine transform with rounding and clipping; the claim that each normalized value is a single token follows directly from the stated assumption that the tokenizer dictionary contains continuous integers from I_min to I_max (Section III.A) and the asserted Tiktoken dictionary coverage of 0-999 (Section IV). That is a derivational step from an unverified premise, not a circular reduction to the paper's own inputs. The 1D search in Section III.B selects sigma_T by minimizing an RMSE-style cost on the first 100 series, and the experimental section says those statistics are used to normalize 'other samples'; although the paper under-specifies whether the reported RMSE tables exclude the calibration subset, the headline improvements are empirical LLM forecasting comparisons rather than algebraic consequences of the fit. The TSFC prompt's motivation cites the author's own submitted work [20], but the prompt's effectiveness is directly measured in Tables 1-3, so the self-citation is motivational rather than load-bearing. The unverified tokenizer-coverage claim and the ambiguous calibration/evaluation split are real correctness and reproducibility risks, but neither makes the derivation circular. No step reduces, by construction or by self-citation, to its own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a factual assumption about the tokenizer's integer coverage, a symmetry assumption for the target mean, a search procedure that tunes sigma_T on the evaluation data, and a single-response stability assumption for the API. All four are unverified in the paper.

free parameters (2)
  • sigma_T (target standard deviation) = 24.57 (AIHEPC), 312.31 (SM4)
    Determined by 1D Golden Section Search minimizing RMSE on the first 100 samples of each dataset; it is a fitted hyperparameter, not derived.
  • m_T (target mean) = 499.5
    Set by hand as (Imin+Imax)/2 under the assumption of symmetric distributions; not fitted but a design choice.
assumptions (4)
  • domain assumption The Tiktoken tokenizer dictionary contains every integer from 0 to 999 as a single token.
    Sections III.A and IV state the dictionary includes integers 0 to 999, but no tokenization analysis is provided to confirm each value encodes as one token.
  • ad hoc to paper Time series values are symmetrically distributed around the midpoint, justifying m_T=499.5.
    Section III.B fixes m_T at (Imin+Imax)/2 because 'numeric values are symmetrically distributed'; this is assumed, not verified for AIHEPC or SM4.
  • domain assumption The LLM cost as a function of sigma_T is unimodal enough for Golden Section Search to find a useful optimum.
    Section III.B applies Golden Section Search while acknowledging non-convexity; no proof that the search converges to a valid local optimum relevant to forecasting.
  • domain assumption GPT-4o-mini responses are stable enough to compare RMSE values without repeated sampling or temperature settings.
    The experiments report single RMSE/MAE values; no sampling configuration or repeated-run statistics are given.

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Cite this review

Pith. "Pith review of TOKON: TOKenization-Optimized Normalization for time series analysis with a large language model." pith.science (2026). https://pith.science/paper/ALZM2WUE

@misc{pith2026250205701,
  author       = {Pith},
  title        = {Pith review of: TOKON: TOKenization-Optimized Normalization for time series analysis with a large language model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ALZM2WUE}},
  note         = {Machine review of arXiv:2502.05701}
}
read the original abstract

While large language models have rapidly evolved towards general artificial intelligence, their versatility in analyzing time series data remains limited. To address this limitation, we propose a novel normalization technique that considers the inherent nature of tokenization. The proposed Tokenization-Optimized Normalization (TOKON) simplifies time series data by representing each element with a single token, effectively reducing the number of tokens by 2 to 3 times. Additionally, we introduce a novel prompt for time series forecasting, termed Time Series Forecasting with Care (TFSC), to further enhance forecasting performance. Experimental results demonstrate that TOKON improves root mean square error (RMSE) for multi-step forecasting by approximately 7% to 18%, depending on the dataset and prompting method. Furthermore, TFSC, when used in conjunction with TOKON, shows additional improvements in forecasting accuracy for certain datasets

Figures

Figures reproduced from arXiv: 2502.05701 by the authors.

Figure 1
Figure 1. 1D Search for TOKON parameterization. IV. EXPERIMENTS Task: A multi-steps forecasting for a univariate time series will be considered. Datasets: The Average IHEPC (AIHEPC) dataset and a subset of the M4 (SM4) training dataset were used to evaluate time series forecasting performance. The AIHEPC dataset, constructed by averaging the global intensity in the Individual Household Electric Power Consumption (IHEPC) datas… view at source ↗
Figure 2
Figure 2. Convergence characteristic with 1D search to determine scale parameter where x axis is the number of iterations and y axis the RMSD Search for TOKON parameterization. Main Results: To assess the efficacy of the TOKON normalization and TSFC prompting, the proposed methods were compared for different datasets. The performance with the AIHEPC dataset is shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Normalized RMSE performance with TOKON at each forecasting step for each prompting and each dataset, where RMSE for each dataset is normalized by the minimum RMSE over steps and prompting methods (x￾axis represents the steps in forecasting and y-axis the normalized RMSE). V. CONCLUSIONS In this paper, a tokenization-optimized normalization and a prompting method for time series forecasting were proposed. The propose… view at source ↗

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Forward citations

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Reference graph

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Reviewed August 8, 2026 · model on record in the stance chip above.