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REVIEW 3 major objections 5 minor 21 references

LMS-AutoTSF: Learnable Multi-Scale Decomposition and Integrated Autocorrelation for Time Series Forecasting

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read LMS-AutoTSF claims state-of-the-art forecasting accuracy using learnable frequency filters and lagged-difference autocorrelation.

desk verdict A useful lightweight forecaster buried under unsupported SOTA claims; the paper's own Table 2 contradicts the headline. read the letter →

arxiv 2412.06866 v3 pith:R5EFSYWC submitted 2024-12-09 cs.LG cs.AI

Ibrahim Delibasoglu , Sanjay Chakraborty , Fredrik Heintz This is my paper · ORCID
classification cs.LGcs.AI
keywords timeseriesforecastinglearnabledecompositionfrequencydomainfilteringautocorrelationmulti-scaleprocessinglightweightarchitecturemultivariateFFT
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

LMS-AutoTSF is a time series forecasting architecture that aims to show a lightweight fully connected network can match or beat transformer-based models. The paper argues that learnable low-pass and high-pass filters in the frequency domain can isolate trend and seasonal components without predefined decomposition, and that multiplying processed features by the first lagged difference injects autocorrelation into the model. If correct, the approach would mean expensive attention mechanisms are not necessary for state-of-the-art long-term and short-term forecasting on standard benchmarks. The paper reports the best or second-best mean squared error on most datasets, along with far lower FLOP counts than transformer baselines.

What carries the argument

The load-bearing mechanism is the dual-encoder-per-scale processing driven by learnable frequency-domain filters: for each of $K$ downsampled scales, a trainable low-pass filter $\sigma(-(f - f_{\text{cutoff}}) s)$ isolates the trend and a trainable high-pass filter $\sigma((f - f_{\text{cutoff}}) s)$ isolates the seasonal component, with cutoff and steepness learned per feature. A second mechanism is the autocorrelation injection of Equation (9), where the temporally processed feature $x_{\text{temp}}$ is multiplied elementwise by the first lagged difference $\Delta T^{(k)}$ of that scale's trend (or seasonal) input, intended to make the network aware of how much the series changes between consecutive steps. The paper's argument that these two mechanisms together produce better predictions than either alone rests on an ablation table showing monotone MSE improvements from fixed decomposition to learnable decomposition to learnable decomposition plus autocorrelation on ETTh1, ETTm1, Weather, and Electricity.

What would settle it

Ablate Equation (9) by replacing $\Delta T^{(k)}$ with a constant vector of ones and retrain on the same eight benchmarks with multiple seeds; if mean squared error does not degrade significantly on most datasets, the claimed benefit of integrated autocorrelation is not supported. The paper's own ablation shows only small gains, e.g., ETTh1 MSE 0.448 to 0.441, with no variance or significance testing.

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Extended reading notes

Core claim

The central claim is that the proposed LMS-AutoTSF architecture achieves state-of-the-art performance in multivariate time series forecasting by combining three mechanisms: multi-scale downsampling of the input, learnable FFT-based low-pass and high-pass filters that decompose each scale into trend and seasonal components, and an autocorrelation term computed as the element-wise product of the temporally processed features with the first lagged difference of the encoder input. The trend and seasonal encoders each use fully connected layers for temporal and channel interactions, and their per-scale forecasts are concatenated and projected to the final prediction. The paper reports that this design outperforms or matches transformer-based models such as iTransformer, PatchTST, and TimeMixer on long-term benchmarks, achieves competitive results on PEMS short-term traffic forecasting, and does so with substantially lower execution time and FLOP counts.

Load-bearing premise

The load-bearing premise is that multiplying the temporally processed features by the first lagged difference of the encoder input is what lets the model capture temporal dependencies; if that elementwise multiplication contributes nothing, the architecture reduces to a multi-scale MLP with learnable frequency filters, and the paper's key innovation claim collapses.

Editorial extensions

If this is right

  • If the central claim holds, fully connected MLP architectures can achieve competitive or better long-term forecasting accuracy than transformer models, suggesting attention is not required for these benchmarks.
  • The reported FLOP and execution-time reductions would make the method suitable for resource-constrained forecasting applications, such as on-device traffic or energy prediction.
  • The learnable frequency-domain decomposition would allow the model to adapt to datasets with different trend-seasonality structures without manual decomposition choices.
  • The simple lagged-difference autocorrelation provides a low-cost alternative to attention for capturing temporal dependencies, one that could be dropped into other MLP forecasters.

Reading between the lines

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

  • If the autocorrelation mechanism is genuinely useful, replacing the fixed one-step difference with learnable lag operators selected by the input's autocorrelation function could improve accuracy further; the paper does not explore this.
  • The efficiency comparison is reported on a single GPU; an independent inference benchmark on CPU or edge hardware would test whether the FLOP advantage translates to real-world deployments.
  • The ablation's small gains suggest the lagged-difference product may matter most on nonstationary series; stratifying results by trend strength (e.g., Exchange vs. Weather) could reveal where the mechanism carries the performance.
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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

3 major / 5 minor

Summary. The paper proposes LMS-AutoTSF, a time series forecasting architecture that combines multi-scale downsampling, learnable FFT-based low-pass and high-pass filters, two fully connected encoders per scale (one for trend, one for seasonality), and an autocorrelation mechanism implemented as element-wise multiplication by a lagged difference. The authors claim that this lightweight, fully connected design achieves state-of-the-art forecasting performance across long-term and short-term benchmarks, and they support this with experiments on ETT, Weather, Electricity, Traffic, Exchange, PEMS, and M4 datasets, including an ablation study and an efficiency comparison.

Significance. If the state-of-the-art claim were supported, the contribution would be notable: a simple, non-transformer, efficient architecture competing with or beating strong baselines would be a useful addition to the forecasting toolbox. The manuscript has genuine strengths: the source code is publicly available, the experimental coverage is broad (eight multivariate long-term datasets, four PEMS datasets, and M4), and the ablation study isolates the proposed components. However, the central empirical claim is substantially overstated relative to the paper's own tables, and the absence of error bars or multiple-seed results makes the reported gains difficult to interpret. The significance of the work is therefore currently limited to a competitive-and-efficient architecture rather than a state-of-the-art one.

major comments (3)
  1. [Section 5.2, Table 2] The claim in Contribution 3 and the Conclusion that LMS-AutoTSF "achieves state-of-the-art performance" and "consistently achieves the best performance across most datasets" is directly contradicted by Table 2. For the average MSE over horizons 96/192/336/720 with look-back 96, FEDformer is better on ETTh1 (0.439 vs. 0.441), ETSFormer is substantially better on ETTm1 (0.304 vs. 0.377), iTransformer is substantially better on Traffic (0.444 vs. 0.497), and DLinear is better on Exchange (0.340 vs. 0.353). The differences on Traffic and Exchange are large, and on the remaining datasets LMS-AutoTSF is often competitive rather than superior. Since the headline contribution is explicitly framed as state-of-the-art, this evidence is load-bearing and must be either corrected or the claim must be reframed as "competitive on many benchmarks while being more efficient."
  2. [Section 1 vs. Section 4 (Eqs. 5-6)] There is an internal inconsistency in the role of the filters. Section 1 states that "low-pass filtering is commonly used to capture seasonal variations" and "high-pass filtering is employed to model trends." In contrast, Section 4, Eq. (5) defines the low-pass filter as capturing the trend, and Eq. (6) defines the high-pass filter as extracting the seasonal component. The two descriptions are exactly reversed. This matters because the paper's first contribution is the "dynamic decomposition" into trend and seasonality; if the authors themselves are not consistent about which filter extracts which component, the reader cannot know what the learned decomposition is actually doing. Please correct the introduction or the method description and make the semantics consistent throughout.
  3. [Table 1, Eq. (9)] The ablation study in Table 1 reports only a single run per configuration, with no error bars, standard deviations, or significance tests. The claimed benefit of the integrated autocorrelation is small: on ETTh1 the MSE goes from 0.448 to 0.441, and on ETTm1 from 0.392 to 0.377, while on Weather and Electricity the differences are tiny (0.240 vs. 0.238 and 0.174 vs. 0.175, respectively). These gaps are within the range of typical run-to-run variability for deep forecasting models, so the contribution of autocorrelation is not established. In addition, Eq. (9) multiplies the processed temporal features by the lagged difference and the text asserts this "enables the model to capture dependencies across time more effectively," but no experiment isolates this operation nor analyzes its effect. Please provide multiple seeds with variance and, ideally, a statistical comparison, or soften the claim about autocorrelation's benefits.
minor comments (5)
  1. [Figure 1] The caption labels the architecture "LMS-AutoTS" while the model name is LMS-AutoTSF; please make the figure consistent with the text.
  2. [Section 4, Eq. (9)] The symbol \Delta T^{(k)} is used for the lagged difference but is never formally defined. Please define it explicitly when it is first introduced.
  3. [Section 5.1] The text refers to a "supplementary file" for dataset details, but no supplementary material is provided in the manuscript; either include the file or remove the reference.
  4. [References] Reference [12] is cited as "Autoformer: Searching transformers for visual recognition," which is a different paper on visual recognition, not the Autoformer time series forecasting paper by Wu et al. Please correct the citation.
  5. [Table 3] The M4 table reports comparisons only against iTransformer, TimeMixer, and PatchTST, but the text says "state-of-the-art models"; this is a limited set, and the conclusion that LMS-AutoTSF is best is not supported by the table, since TimeMixer has lower average sMAPE and MAPE.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the pipeline is trained and tested on external benchmarks, and no predicted quantity reduces to a fitted input or self-citation.

full rationale

LMS-AutoTSF is an empirical architecture paper. Its central claim ("LMS-AutoTSF consistently achieves state-of-the-art performance across a wide range of benchmarks") is supported by test-set MSE/MAE comparisons against independently published baselines; these comparisons are external evidence, not consequences of the model's own equations or of the authors' prior work. The learnable FFT low/high-pass filters (Eqs. 5-6), multi-scale downsampling (Eq. 2), and autocorrelation gate (Eq. 9) are all transformations applied to input data; their parameters are fitted on training folds, and the reported errors are measured on held-out test sets. No quantity that is defined in terms of the target is later "predicted" as if independent, and no parameter fitted to a subset is reported as a prediction on that subset. The reference list contains no overlapping author self-citations and no uniqueness theorem is invoked to force a choice. The paper does contain internal inconsistencies and robustness concerns: the introduction assigns low-pass filtering to seasonality while Section 4 assigns low-pass filtering to trend, and Table 2 shows LMS-AutoTSF is not the best on ETTh1, ETTm1, Traffic, or Exchange, so the unqualified SOTA claim is not supported as written. Those are correctness and presentation issues, not circularity. The ablation also lacks error bars or significance tests, but that weakens evidence strength rather than making the derivation circular. The claimed derivation is therefore self-contained against external benchmarks, and the appropriate circularity finding is no significant circularity.

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

The central claim rests on standard ML components plus two learnable filter parameters, a hand-chosen scale count, and an ad hoc differencing operation. No new physical entities are introduced. The additive decomposition and average-pooling preservation are domain assumptions that are not tested. The main ad hoc element is the 'autocorrelation' term, which is a first difference that the paper does not justify theoretically.

free parameters (4)
  • Filter cutoff frequency f_cutoff
    Learnable per-feature cutoff for the low-pass and high-pass sigmoid masks (Eq. 5-6); optimized on training data.
  • Filter steepness s
    Learnable steepness of the sigmoid mask in the frequency domain (Eq. 5-6).
  • Number of scales K = 4
    Set to 4 without ablation or sensitivity analysis; chosen by hand (Section 5).
  • Look-back window L = 96
    Fixed at 96 for all long-term experiments; not swept, though it is a standard choice in the baselines.
assumptions (4)
  • domain assumption Time series decomposes additively as trend plus seasonal components (Eq. 7).
    The entire dual-encoder design assumes X = T + S, with no multiplicative or interaction terms modeled.
  • domain assumption Average-pooling downsampling preserves the information needed for forecasting (Eq. 2).
    Multi-scale inputs are created by average pooling, which by design discards high-frequency detail at coarser scales.
  • ad hoc to paper Element-wise multiplication by the first lagged difference improves temporal modeling (Eq. 9).
    The paper labels this operation autocorrelation and asserts a benefit, but provides no derivation and only a single ablation row without variance.
  • standard math FFT and inverse FFT are exact and differentiable for the masking operation.
    The method relies on standard FFT properties; this is a safe background assumption.

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Cite this review

Pith. "Pith review of LMS-AutoTSF: Learnable Multi-Scale Decomposition and Integrated Autocorrelation for Time Series Forecasting." pith.science (2026). https://pith.science/paper/R5EFSYWC

@misc{pith2026241206866,
  author       = {Pith},
  title        = {Pith review of: LMS-AutoTSF: Learnable Multi-Scale Decomposition and Integrated Autocorrelation for Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R5EFSYWC}},
  note         = {Machine review of arXiv:2412.06866}
}
read the original abstract

Time series forecasting is an important challenge with significant applications in areas such as weather prediction, stock market analysis, scientific simulations and industrial process analysis. In this work, we introduce LMS-AutoTSF, a novel time series forecasting architecture that incorporates autocorrelation while leveraging dual encoders operating at multiple scales. Unlike models that rely on predefined trend and seasonal components, LMS-AutoTSF employs two separate encoders per scale: one focusing on low-pass filtering to capture trends and the other utilizing high-pass filtering to model seasonal variations. These filters are learnable, allowing the model to dynamically adapt and isolate trend and seasonal components directly in the frequency domain. A key innovation in our approach is the integration of autocorrelation, achieved by computing lagged differences in time steps, which enables the model to capture dependencies across time more effectively. Each encoder processes the input through fully connected layers to handle temporal and channel interactions. By combining frequency-domain filtering, autocorrelation-based temporal modeling, and channel-wise transformations, LMS-AutoTSF not only accurately captures long-term dependencies and fine-grained patterns but also operates more efficiently compared to other state-of-the-art methods. Its lightweight design ensures faster processing while maintaining high precision in forecasting across diverse time horizons. The source code is publicly available at \url{http://github.com/mribrahim/LMS-TSF}

Figures

Figures reproduced from arXiv: 2412.06866 by the authors.

Figure 1
Figure 1. (a) Overall architecture of LMS-AutoTS. (b) Encoder module operations for trend and seasonal components [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. It represents a broader analysis of the methods’ [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 2
Figure 2. Comparison of models efficiency with datasets vs. avg. MSE vs. avg. MAE [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: Visualization of prediction results on ETTh2 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 5
Figure 5. Figure 5: Visualization of prediction results on PEMS03 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 4
Figure 4. Figure 4: Visualization of prediction results on Electricity [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

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Reference graph

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