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REVIEW 4 major objections 8 minor 2 cited by

EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions

T0 review · 4 major / 8 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read EDformer claims that decomposing a multivariate series into trend and seasonal parts, embedding each variable's whole series as a token, and applying self-attention across variables yields state-of-the-art forecasts with lower compute.

desk verdict The architecture is a clean iTransformer-plus-decomposition combo, but the paper's own Table V contradicts its state-of-the-art claim, so it doesn't hold up. read the letter →

arxiv 2412.12227 v1 pith:FTNHA6ZH submitted 2024-12-16 cs.LG cs.AI

Sanjay Chakraborty , Ibrahim Delibasoglu , Fredrik Heintz This is my paper · ORCID
classification cs.LGcs.AI
keywords time-seriesforecastingmultivariatetransformerencoderseasonal-trenddecompositionvariate-as-tokenembeddingexplainableAIefficiency
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 introduces EDformer, an encoder-only Transformer for multivariate time series forecasting, and claims it reaches state-of-the-art accuracy and speed on standard long-term and short-term benchmarks. The method first decomposes each input into a seasonal part and a trend part with a moving average, then treats each variable's entire series as one token rather than using time-step tokens. Self-attention runs across variables, while a shared feed-forward network processes each variable's series to learn its temporal structure; the trend is added back before the final projection. A sympathetic reader should take the contribution as this specific combination of decomposition and variate-as-token attention, supported by ablations and explainability analyses.

What carries the argument

The central mechanism is the variate token formed by the reverse operation: instead of one token per time step, each variable's whole seasonal and trend series is embedded as one token, so the token dimension is the number of variables. Eq. (5) defines the update: $h^0_n = \mathrm{Embedding}(\mathrm{Reverse}(X^S_{:,n})) + \mathrm{Embedding}(\mathrm{Reverse}(X^T_{:,n}))$, then $H^{(l+1)} = \mathrm{IntBlock}(H^l)$ and the forecast is $\hat{Y}_{:,n} = \mathrm{Projection}(h^L_n)$. The multivariate self-attention block computes attention scores $\frac{QK^T}{\sqrt{d_k}}$ across variate tokens, while the shared feed-forward network $\mathrm{FFN}(H') = \mathrm{ReLU}(H'W_1 + b_1)W_2 + b_2$ processes each variate's representation separately. This division of labor is what lets EDformer drop temporal attention and positional encoding.

What would settle it

Re-run the ETTh1 horizon-96 comparison with the strongest baseline at its officially released hyperparameters: if EDformer's reported MSE of 0.404 does not beat the baseline's published MSE under identical splits, the state-of-the-art claim collapses; likewise, the no-decomposition ablation's average MSE of 1.010 on ETTh1 should not be worse than a simple linear forecaster.

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Extended reading notes

Core claim

The paper's central claim is that an encoder-only Transformer with the same basic components can reach state-of-the-art multivariate forecasting if the components are used differently: decompose each input into trend and seasonal parts, embed each variable's entire seasonal series as a single token, run self-attention across variables, pass each variable's representation through a shared feed-forward network, then add the projected trend back. The decomposition is $X_T = \mathrm{AvgPooling}(\mathrm{Padding}(X))$, $X_S = X - X_T$; the token update is $h^0_n = \mathrm{Embedding}(\mathrm{Reverse}(X^S_{:,n})) + \mathrm{Embedding}(\mathrm{Reverse}(X^T_{:,n}))$, followed by stacked blocks of multivariate self-attention and feed-forward layers before projection. Attention therefore captures cross-variate correlations while the feed-forward network stores temporal structure, and no positional encoding is needed because the per-variate MLP preserves sequence order.

Load-bearing premise

The load-bearing premise is that the comparison baselines were faithfully reimplemented and equally tuned; if they were undertuned, the reported accuracy gains are artifacts rather than real improvements.

Editorial extensions

If this is right

  • On most long-term benchmarks and horizons, EDformer reports lower average MSE and MAE than the compared transformer baselines, with the largest gains on high-dimensional datasets such as Electricity and Traffic.
  • EDformer's per-iteration and total execution times are substantially lower than the compared models, so it can be retrained more often and used in settings with limited compute.
  • Ablations show that both decomposition and reverse embedding contribute to accuracy, and their combination is better than either alone.
  • On Electricity, EDformer scores highest on comprehensiveness and sufficiency across five explainability methods, indicating that its predictions track the features that attribution methods flag as important.
  • The efficiency result implies that the model can be updated more frequently on streaming data, making it feasible for near-real-time forecasting workflows.

Reading between the lines

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

  • If the reported speed holds, the decomposition-plus-variate-token recipe could be grafted onto other encoder-only forecasters to cut the cost of temporal attention, not just as a standalone model.
  • The ablation suggests decomposition alone already helps; a natural test is whether the order of decomposition and reverse embedding matters, or whether a simpler per-variate MLP with trend addition matches EDformer.
  • The high sufficiency scores on Electricity imply EDformer concentrates predictive signal in a few features; a testable extension is to prune low-attribution channels and measure accuracy retention.
  • Because the paper provides no code or baseline configurations, an immediate extension is to check how EDformer behaves when compared against baselines at their officially tuned settings.
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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 / 8 minor

Summary. The paper proposes EDformer, an encoder-only transformer for multivariate time series forecasting. It decomposes the input into seasonal and trend components, embeds each variate's entire series as a token using a reverse/inverted embedding, applies self-attention across variates and a feed-forward network per variate, and adds the trend component back at the end. The authors report long-term results on eight benchmarks, short-term results on PEMS and M4, efficiency measurements, ablations, and an explainability analysis. They claim that EDformer achieves state-of-the-art accuracy and efficiency and that its decomposition and reverse embedding are key to its performance.

Significance. The architectural idea of combining series decomposition with an inverted transformer is a reasonable incremental direction, and the paper provides a substantial set of experiments: standard benchmarks, ablations, runtime tables, and an explainability evaluation on Electricity. The paper also names its implementation environment and uses public datasets. However, the central accuracy claim is contradicted by the paper's own Table V, where ATFNet achieves lower average MSE on five of eight datasets. The comparison also omits iTransformer, the direct predecessor of the variate-token design, making the incremental value difficult to assess. As presented, the evidence does not support the headline state-of-the-art claim; this is a load-bearing issue rather than a presentational one.

major comments (4)
  1. [Abstract; Section V.B; Table V] The state-of-the-art accuracy claim is contradicted by the paper's own averaged results in Table V. Averaging over horizons 96, 192, 336, and 720, ATFNet reports lower average MSE than EDformer on ETTh1 (0.515 vs 0.594), ETTh2 (0.252 vs 0.538), ETTm2 (0.169 vs 0.543), Weather (0.229 vs 0.304), and Exchange (0.436 vs 0.537), and lower average MAE on six of the eight datasets. The # of Total Wins row records only a 3-3 tie in MSE. Thus the claim that EDformer obtains state-of-the-art accuracy is not supported by the data presented.
  2. [Section IV.B; Section V.B; Tables V and VIII] The main multivariate long-term comparison omits iTransformer, even though Section IV.B identifies iTransformer as the inspiration for the variate-frame design and iTransformer appears only in the M4 supplementary table (Table VIII). Since EDformer's mechanism is essentially an inverted transformer plus a decomposition block, the absence of iTransformer from the long-term benchmark tables prevents the reader from assessing the incremental contribution of the proposed modifications. Without this baseline, the state-of-the-art claim is not actionable.
  3. [Section VI; Table XI] The ablation results suggest that the baseline implementations may be undertuned. The 'without decomposition' configuration reaches an average MSE of 1.010 on ETTh1 and 0.905 on ETTm1, which is substantially worse than published results for the same underlying inverted-transformer design (e.g., iTransformer reports an average MSE of about 0.5 on ETTh1). Because the paper states that baselines were reimplemented via TSLib (Section V.B), the discrepancy needs to be resolved by releasing exact configurations and hyperparameters; otherwise the reported gains from decomposition and reverse embedding may be artifacts of a weak base rather than genuine improvements.
  4. [Section V.B; Tables IX and X] The efficiency claim is not established against the relevant state of the art. Tables IX and X compare EDformer with Autoformer, Informer, Reformer, Pyraformer, FEDformer, and NS-Trans, but omit comparably lightweight and high-performing models such as iTransformer and PatchTST. Showing that EDformer is faster than deliberately heavy architectures does not support the stated claim of state-of-the-art efficiency; the runtime comparison needs to include the models that are actually competitive in accuracy.
minor comments (8)
  1. [Table VI] Table VI is labeled 'Comparison of Standard deviations ... with prediction horizons (96,192,336,720)'; the numbers appear to be standard deviations across the four horizons, but the text does not specify this, nor does it clarify whether the standard deviation is computed over seeds or horizons. Please state the statistic explicitly.
  2. [Section V.B; Table VII] The text says EDformer has 'competitive performance' in short-term forecasting on PEMS, but Table VII shows that NS-Trans is clearly better on all four PEMS datasets (e.g., PEMS03 MSE 0.106 vs 0.187). Rephrase to reflect the actual results.
  3. [Section III] Equation (1) uses inconsistent notation: X_t is defined in R^{T x N}, but the history is called X_{t-l} and the future X_{t+h}, and the look-back window L and horizon H are not tied to these expressions. Please unify the notation.
  4. [Section IV.A] Equation (4) writes the input as X in R^{L x D}, while Section III defines the input as R^{T x N}; the dimensions and symbols should be consistent across the problem statement and the architecture description.
  5. [Section IV.C.1] The sentence following Equation (7) is incomplete: 'where n represents an input sequence of length...'. Also, the complexity O(n^2 d) should identify n as the number of variates in the inverted design, not the temporal sequence length.
  6. [Section VII.A; Tables XII-XV] The interpretability tables report MAE and MSE values but describe higher values as better for comprehensiveness and sufficiency. Since MAE and MSE are error metrics where lower is better, the direction of the 'wins' needs to be justified and explained; otherwise the reader cannot interpret which model benefits most from an explainability method.
  7. [Reference [12]] Reference [12] is listed as 'Autoformer: Searching transformers for visual recognition' and is used in the text as the Autoformer time-series forecasting paper. The actual time-series Autoformer paper should be cited instead.
  8. [Section IV.B] The 'reverse' operation in the embedding is never formally defined. The text says 'reverse embedding' but does not specify the mathematical transformation, making the method difficult to reproduce.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: EDformer's decomposition and forecasting pipeline is a standard supervised learning construction; the SOTA accuracy overclaim is an empirical/correctness issue, not a derivation-from-inputs issue.

full rationale

The paper's derivation chain is a standard supervised forecasting pipeline: the input series is decomposed in Eq. (4) by defining the trend as an average-pooled version of the input and the seasonal component as the residual; each variate is then embedded as a token, processed by self-attention and feed-forward blocks, projected, and finally recombined with the trend. No fitted constant or fitted parameter is later relabeled as a prediction, and no equation reduces to another by construction. The forecasting evaluation uses public datasets with held-out test splits, so the reported MSE/MAE values are empirical outcomes rather than consequences of the model definition. The ablation study in Table XI compares configurations and is not circular. The paper's 'state-of-the-art' claim is contradicted by its own Table V, where ATFNet achieves lower average MSE on several datasets, but that is a correctness or internal-consistency problem, not a circularity problem. The citation of iTransformer is only for architectural inspiration and is not load-bearing in the sense of a self-citation chain or an imported uniqueness theorem. The explainability analysis is an evaluation of attribution methods, not a source of predictions. Therefore, no significant circularity is present.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The model introduces no new physical or mathematical entities. Its free parameters are standard neural network hyperparameters, several of which are not reported in the paper. The key assumptions are the representativeness of the benchmarks, the faithfulness of the reimplemented baselines, and the sufficiency of the additive trend/seasonal decomposition.

free parameters (5)
  • AvgPooling kernel size (moving average window) = not reported
    Used in Eq. (4) to extract the trend component. The paper does not specify the kernel size, which controls the trend/seasonal split and directly affects forecasting performance.
  • Embedding dimension D = not reported
    Dimension of the variate tokens in Eq. (5); central to model capacity and never stated in the paper.
  • Number of encoder layers (IntBlocks) = not reported
    Depth of the encoder stack in Eq. (5); no value is given despite the equation using L for the number of blocks, which also clashes with the lookback length L.
  • Number of attention heads = not reported
    Multi-head attention is used in Eq. (10), but the head count is not reported.
  • K (number of scales) = 4
    Section V-B states 'The model operates with K = 4 scales', but no definition of K or its role in the architecture is provided.
assumptions (4)
  • domain assumption The standard benchmarks (ETT, Weather, Electricity, Traffic, Exchange, PEMS, M4) and their train/test splits are representative of the multivariate time series forecasting problem.
    The paper draws all conclusions from these datasets without external validation on other domains.
  • domain assumption The reimplemented baseline models are faithful to their original publications and fairly tuned.
    The authors state they replicated baselines using the 'Time-Series Library (TSLib)'; no code or configurations are given, and the ablation baseline 'without decomposition' is far worse than published iTransformer results, suggesting possible undertuning.
  • domain assumption The moving-average decomposition (Eq. 4) separates the signal into trend and seasonal parts that are each individually learnable and additively sufficient for forecasting.
    The entire architecture rests on this decomposition; if the additive trend/seasonal split is inappropriate for a dataset, the model's performance would degrade.
  • domain assumption Treating each variate's entire lookback series as a single token preserves the temporal information needed for forecasting.
    This is the inverted-transformer assumption from iTransformer, adopted without new justification.

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Cite this review

Pith. "Pith review of EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions." pith.science (2026). https://pith.science/paper/FTNHA6ZH

@misc{pith2026241212227,
  author       = {Pith},
  title        = {Pith review of: EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FTNHA6ZH}},
  note         = {Machine review of arXiv:2412.12227}
}
read the original abstract

Time series forecasting is a crucial challenge with significant applications in areas such as weather prediction, stock market analysis, and scientific simulations. This paper introduces an embedded decomposed transformer, 'EDformer', for multivariate time series forecasting tasks. Without altering the fundamental elements, we reuse the Transformer architecture and consider the capable functions of its constituent parts in this work. Edformer first decomposes the input multivariate signal into seasonal and trend components. Next, the prominent multivariate seasonal component is reconstructed across the reverse dimensions, followed by applying the attention mechanism and feed-forward network in the encoder stage. In particular, the feed-forward network is used for each variable frame to learn nonlinear representations, while the attention mechanism uses the time points of individual seasonal series embedded within variate frames to capture multivariate correlations. Therefore, the trend signal is added with projection and performs the final forecasting. The EDformer model obtains state-of-the-art predicting results in terms of accuracy and efficiency on complex real-world time series datasets. This paper also addresses model explainability techniques to provide insights into how the model makes its predictions and why specific features or time steps are important, enhancing the interpretability and trustworthiness of the forecasting results.

Figures

Figures reproduced from arXiv: 2412.12227 by the authors.

Figure 1
Figure 1. Overall architecture of EDformer breaking down a time series into three systematic components: trend-cycle, seasonal variation, and random fluctuations. The trend component reflects the long-term direction of the series, which may be increasing, decreasing, or stable over time. The seasonal component captures recurring patterns within the series, while the random (or ”irregular”) component accounts for noise that ca… view at source ↗
Figure 2
Figure 2. Internal architecture of EDformer blocks [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Visualization of predictions (length:96) on ETTm1 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (4 more)
Figure 6
Figure 6. Figure 6: Visualization of prediction results on PEMS03 dataset [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 5
Figure 5. Figure 5: Visualization of predictions (length:96) on Traffic [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 7
Figure 7. Figure 7: Comparison on execution time (minutes) for model [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Feature importance of EDformer model on the electric [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. CaReTS: A Multi-Task Framework Unifying Classification and Regression for Time Series Forecasting

    cs.LG 2025-11 conditional novelty 5.0 of 10

    CaReTS forecasts multi-step time series by combining a trend classifier with a deviation regressor in a residual, uncertainty-weighted multi-task framework.

  2. A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations

    cs.IR 2026-07 reject novelty 4.0 of 10

    A trainable 6-qubit-per-channel variational circuit plus linear readout roughly matches transformer forecasters at short horizons on ETT/Weather/Electricity benchmarks, but the reported setup does not match the paper'...

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.