A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting

Boshi Gao; Fanbo Ju; Qingjian Ni; Yu Chen; Ziqi Zhao

REVIEW 3 major objections 5 minor 43 references

A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read MDMixer claims a 4.64% average MAE improvement over the MLP state of the art (TimeMixer) on eight long-term forecasting benchmarks, with lower training cost.

desk verdict MDMixer is a plausible incremental architecture, but its headline MAE margin over TimeMixer is largely a training-objective artifact and the SOTA claim does not survive close reading. read the letter →

arxiv 2505.08199 v2 pith:5T2FHFBQ submitted 2025-05-13 cs.LG

Boshi Gao , Qingjian Ni , Fanbo Ju , Yu Chen , Ziqi Zhao This is my paper · ORCID

classification cs.LG

keywords long-termtimeseriesforecastingmulti-granularityrepresentationMLP-basedseasonal-trenddecompositionadaptiveweightinggatechannel-dependentfusionmulti-scalepredictionefficiency

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

This paper tries to establish that long-term time series forecasting improves when a model explicitly predicts the series at several temporal granularities at once and then lets each data channel decide how much to trust each granularity. The proposed MDMixer architecture runs parallel prediction heads at graduated lengths, mixes them coarse-to-fine, and fuses them with a channel-dependent gating network, on top of a trend/seasonal dual branch. On eight standard benchmarks, the paper reports that this beats the previous best MLP forecaster, TimeMixer, by 2.50% in MSE and 4.64% in MAE on average, while using far less training time and memory than comparable models. The authors also claim the dual-branch design can be transplanted into existing linear models to improve them. A sympathetic reader would care because it suggests simple, efficient MLP architectures can outperform attention-based models without giving up interpretability.

What carries the argument

The load-bearing mechanism is the Multi-granularity Predictor and Mixer (MPM) block, made of three interacting pieces: MPP, where parallel heads predict at graduated lengths so the model explicitly represents coarse seasonal/trend behavior and fine fluctuations at once; MIM, which iteratively fuses the heads coarse-to-fine by adding each head's output to a linear transformation of the previous cumulative output; and AMWG, a gating network that takes global average-pooled seasonal and trend embeddings, concatenates them, and produces an $H \times C$ weight tensor, with softmax over heads per channel. A dual-branch decomposition routes the seasonal component through linear predictors and the trend through MLPs, and an auxiliary alignment loss compares each intermediate prediction with a downsampled target. The final prediction is the channel-weighted sum of upsampled head outputs plus their unweighted average, which acts as a stable baseline.

What would settle it

Run TimeMixer, iTransformer, PatchTST, and MDMixer on all eight datasets under one shared codebase, same hardware, same seeds, same normalization, and the same hyperparameter search budget; if TimeMixer's average MAE matches or beats MDMixer, or the gap disappears within seed noise, the central improvement claim fails.

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Extended reading notes

Core claim

The central claim is that multi-granularity information should be generated, not just extracted: MDMixer uses a Multi-granularity Parallel Predictor (MPP) whose $H$ heads each output a prediction of length $G_i = g \cdot i$, so coarse and fine views are produced concurrently from the embedded input; a Multi-granularity Iterative Mixer (MIM) then accumulates these predictions coarse-to-fine; and an Adaptive Multi-granularity Weighting Gate (AMWG) assigns softmax-normalized weights over heads for each channel, allowing different variables to rely on different scales. The trend and seasonal components are modeled separately, with linear layers for seasonality and MLPs for trend, and a granularity-aligned loss supervises each intermediate prediction against a downsampled ground truth. The paper reports that this architecture improves average MAE by 4.64% over TimeMixer across eight LTSF benchmarks, also outperforming iTransformer and PatchTST, and that the dual-branch decomposition improves DLinear, RLinear, and NLinear when inserted into them.

Load-bearing premise

The reported 4.64% MAE margin assumes the baseline numbers taken from prior papers are accurate and comparable; baselines were not re-run by the authors, while MDMixer's numbers are three-seed averages from their own runs, so a same-protocol rerun could shrink or reverse the gap.

Editorial extensions

If this is right

If MDMixer's results hold, MLP-based forecasting can match or beat transformer models on standard LTSF benchmarks while using a fraction of the training time and memory.
The dual-branch decomposition is claimed to be a transferable module: adding it to DLinear, RLinear, and NLinear improves their accuracy, so existing linear baselines can be upgraded without a full architecture change.
The AMWG weight heatmaps show sparse assignments, with most channels concentrating weight on the coarsest and finest heads; this gives users a per-variable diagnostic of which temporal scale drives each channel.
Longer look-back lengths consistently help MDMixer, unlike attention models, so users with long histories can expect better forecasts as history grows.

Reading between the lines

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

If the gating mechanism is the active ingredient, the same AMWG module could be grafted onto TimeMixer or other multi-scale mixers; the paper does not test this, but the ablation evidence makes it worth trying.
The alignment loss uses average-pooled targets, so a natural untested variant would use frequency-selective downsampling to force each head to specialize on a cleaner temporal scale.
The sparse head weights on Electricity suggest that head specialization may correspond to interpretable periodic bands; a spectral analysis of each head's learned mapping would test whether the granularity labels are meaningful.
Because the reported margin is averaged over eight datasets with very different channel counts, a per-dataset breakdown would show whether channel-aware fusion matters most in high-dimensional settings like Traffic and Electricity.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague —

MDMixer is a plausible incremental MLP architecture with one genuinely useful idea: channel-dependent gating across multi-granularity heads, combined with separate linear/MLP branches for seasonal and trend. The paper is clearly written, the ablations give each component a reason to exist, and the dual-branch transplant experiment on DLinear/RLinear/NLinear is a nice way to test the idea outside the full model.

That said, the headline result is weaker than it looks, and the stress-test note is right: MDMixer is trained with L1 loss (Sec 3.5; Sec 4.1.3) while the baseline numbers come from papers that optimized MSE. Table 2 has the fingerprint—MDMixer frequently has worse MSE but better MAE than TimeMixer (ETTh1 96/192, Traffic all horizons), and the aggregate MAE gain (4.64%) is nearly double the MSE gain (2.50%). That is what direct L1 optimization does. The authors never disclose the baselines' training losses or retrain them under the same objective, so the 4.64% claim should not be read as an architecture comparison. A fixed version would retrain baselines with MAE or train MDMixer with MSE and report both.

Minor but related: no standard deviations despite three seeds, no code release, and the "Improvement" row averages percentages over heterogeneous dataset-horizon cells. The SOTA claim in the contributions is also too strong: on Traffic, iTransformer has lower average MAE (0.282 vs 0.286), and on Electricity it wins some MSE cells.

What is actually new is the MPP/MIM/AMWG package, and the paper is honest enough in its ablation to show that removing MPP or AMWG hurts. The efficiency comparison is fair within its limits, and the interpretability heatmap is illustrative rather than deep. All soft spots are fixable. The core architecture does not seem to rest on a circular or invented result.

This is a paper for LTSF practitioners and for anyone who cares about fair benchmarking in time series. It deserves a serious referee, not a desk reject, because the architecture is coherent and the flaw is in the evaluation protocol rather than in the derivation. I would send it back for major revision: disclose or fix the optimization-objective mismatch, release code, report variance, and soften the SOTA wording. If those are addressed, it becomes a solid applied contribution.

Referee Report

3 major / 5 minor

Summary. The paper proposes MDMixer, an MLP-based framework for long-term time series forecasting. The architecture combines multi-granularity parallel prediction heads (MPP), iterative coarse-to-fine mixing (MIM), a channel-dependent adaptive weighting gate (AMWG), and a dual-branch trend/seasonal decomposition with linear and MLP predictors. An auxiliary alignment loss supervises intermediate predictions against downsampled ground truth. Experiments on eight standard benchmarks report an average MAE improvement of 4.64% over TimeMixer, along with improved training efficiency and an interpretability visualization. The paper also shows that adding its dual-branch decomposition to linear baselines improves their accuracy.

Significance. If the reported comparison were clean, MDMixer would be a useful contribution: the architecture is clearly described, the ablation study isolates the role of each module, the sensitivity analyses cover key hyperparameters, and the efficiency comparison is instructive. The paper's central quantitative claim, however, is the 4.64% average MAE improvement over TimeMixer, and that claim is directly affected by a training-loss mismatch between MDMixer and the baselines. The 'state-of-the-art' wording is also broader than the evidence in Table 2 supports. These issues are fixable, but they require either additional experiments or a substantial restatement of the claims.

major comments (3)

[Section 4.1.3 and Table 2] The headline comparison is confounded by a training-loss mismatch. Section 4.1.3 states 'We use MAE as the loss function', and Section 3.5 (Eq. 17) defines the main loss as the L1 norm. The baseline numbers in Table 2 are taken from prior publications, which typically optimize MSE, and the paper does not disclose those losses or retrain baselines under the same objective. Since the abstract's central claim is specifically a 4.64% average MAE improvement over TimeMixer, this is not an architecture-matched comparison. The pattern in Table 2 is consistent with the confound: MDMixer frequently shows better MAE but worse or comparable MSE than TimeMixer (e.g., ETTh1 horizon 96: MAE 0.386 vs 0.400 while MSE 0.379 vs 0.375; Traffic horizon 96: MAE 0.275 vs 0.285 while MSE 0.439 vs 0.462). The authors should retrain baselines with L1 loss, or at minimum report an MSE-based comparison and temper the MAE-based claim accordingly.
[Section 4.1.4 and Table 2] The claim of state-of-the-art performance is not supported by the paper's own table. On Traffic, iTransformer achieves better average MSE and MAE (0.428/0.282) than MDMixer (0.465/0.286), and MDMixer is worse than iTransformer on every Traffic horizon. Similarly, on Electricity with horizon 96, iTransformer has MSE 0.148 versus MDMixer's 0.152. The contribution list and conclusion describe MDMixer as 'state-of-the-art' without qualification, but the evidence only supports a comparison against TimeMixer and specific baselines on some datasets. These sweeping claims should be replaced with dataset-specific statements.
[Section 4.1.3 and 'Improvement' row in Table 2] The empirical significance of the claimed improvements is not established because no standard deviations are reported despite the statement that each experiment was repeated three times, and the baseline numbers have no error bars at all. The 'Improvement' row also averages over heterogeneous per-dataset averages without weighting or noting that MDMixer is worse than iTransformer on Traffic in all four horizons. Given that the claimed improvement margins are on the order of 2–5%, the absence of any variability or significance measure makes it impossible to judge whether the differences are meaningful. The authors should report per-cell standard deviations and clearly define the aggregation procedure.

minor comments (5)

[Section 4.2] The sentence 'our method requires fewer parameters (50.2K vs. 34.8K in the Electricity dataset)' appears to state the numbers in the wrong order; as written it says MDMixer requires more parameters when the comparison presumably intends fewer. Please correct to '34.8K vs. 50.2K' or provide the actual values.
[Figure 5] The caption says 'MSE scores with varying alignment loss weight' but the figure shows both MSE and MAE curves; update the caption to mention both metrics.
[Section 4.5] The efficiency comparison says all models use the same batch size and look-back length but does not state the actual batch size, input length, or model-specific hyperparameter settings. Reporting these details would make the efficiency claim reproducible.
[Section 4.1.4, Table 2] The 'Improvement' row should explain that the percentage is computed as the average of per-dataset averages, not as a reduction on the pooled dataset. This will help readers interpret the aggregate numbers.
[Table 3 caption] The table caption and text use 'vanilla version', 'modified baselines', and asterisks in a way that is easy to confuse. Clarify that asterisks denote baselines augmented with the decomposition module and that '(Dual-Branch)' denotes the proposed replacement of the trend predictor.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: MDMixer's architecture and results are evaluated against external benchmarks, and no prediction reduces to fitted inputs or self-citations.

full rationale

The paper's central claim is an empirical performance comparison against established external baselines on eight standard benchmarks. The method is a new architecture with multi-granularity prediction heads, a mixing module, and a gating mechanism; the final prediction is produced from learned transformations of the input and is not defined in terms of the target quantity. The alignment loss (Eq. 18) supervises intermediate heads with downsampled ground truth, but this is standard auxiliary supervision and does not make the final output equivalent to the target by construction. There are no load-bearing self-citations, no imported uniqueness theorems, and no fitted parameter that is later renamed as a prediction. The reported MAE improvement over TimeMixer is potentially confounded because MDMixer is trained with an L1 loss while baseline numbers were taken from publications that optimize MSE; however, this is an experimental comparability and fairness concern, not a circularity of the derivation chain. The interpretability discussion is a post hoc observation of learned weights and does not feed back into the results. No specific equation-to-equation reduction or self-referential justification was found, so the appropriate finding is no significant circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim is an empirical architecture performance claim, not a derivation. The free parameters are hyperparameters tuned on validation sets. The axioms are standard tools from the time series forecasting literature, with no speculative physical entities introduced.

free parameters (6)

hidden_size = 64 (128 for Electricity and Traffic)
Chosen by hand; larger datasets use 128.
patch_length = 32
Selected from sensitivity analysis in Figure 6; 32 gives lowest MSE.
stride = 16
Set to half the patch length; not independently tuned.
num_heads = 8 (16 for Electricity and Traffic)
Selected from sensitivity analysis in Figure 4; 8 is the default.
alignment_loss_weight = 0.01
Selected from sensitivity analysis in Figure 5.
learning_rate = 1e-2 or 1e-3
Not specified per dataset; a free optimization choice.

assumptions (5)

standard math MLPs are universal approximators
Invoked to justify MLP-based trend modeling (Section 3.2, reference [12]).
domain assumption Linear models capture seasonal periodicities better than MLPs, and MLPs capture trends better
Adopted from prior work [16]; the paper relies on this asymmetry for its dual-branch design (Section 3.2).
domain assumption Instance normalization mitigates distribution shift
Used as a preprocessing step (Section 3.1.1), based on prior work [14,27].
domain assumption Patch embedding preserves useful local temporal structure
Standard practice from PatchTST; assumed to help representation learning (Section 3.2).
domain assumption The benchmark datasets and chronological splits are representative of real-world forecasting
The evaluation protocol follows prior work (Section 4.1.1) and assumes the reported numbers transfer to other settings.

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Cite this review

Pith. "Pith review of A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting." pith.science (2026). https://pith.science/paper/5T2FHFBQ

@misc{pith2026250508199,
  author       = {Pith},
  title        = {Pith review of: A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5T2FHFBQ}},
  note         = {Machine review of arXiv:2505.08199}
}

read the original abstract

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and inherent multi-scale variations within time series. This work confronts key issues in LTSF, including the suboptimal use of multi-granularity information, the neglect of channel-specific attributes, and the unique nature of trend and seasonal components, by introducing a proficient MLP-based forecasting framework. Our method adeptly disentangles complex temporal dynamics using clear, concurrent predictions across various scales. These multi-scale forecasts are then skillfully integrated through a system that dynamically assigns importance to information from different granularities, sensitive to individual channel characteristics. To manage the specific features of temporal patterns, a two-pronged structure is utilized to model trend and seasonal elements independently. Experimental results on eight LTSF benchmarks demonstrate that MDMixer improves average MAE performance by 4.64% compared to the recent state-of-the-art MLP-based method (TimeMixer), while achieving an effective balance between training efficiency and model interpretability.

Figures

Figures reproduced from arXiv: 2505.08199 by the authors.

**Figure 2.** Overview of MDMixer architecture. Multivariate time series are decomposed into trend and seasonal components. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** MSE scores with varying heads number 𝐻 ∈ {2, 4, 8, 12, 16}. 0.001 0.010 0.050 0.100 0.200 Alignment Loss Weight ( ) 0.3085 0.3090 0.3095 0.3100 0.3105 MSE MSE MAE 0.3390 0.3395 0.3400 0.3405 0.3410 MAE ETTm1 0.001 0.010 0.050 0.100 0.200 Alignment Loss Weight ( ) 0.152 0.154 0.156 0.158 0.160 MSE MSE MAE 0.192 0.194 0.196 MAE weather [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 6.** Figure 6: MSE scores with varying patch length 𝑃 ∈ {8, 12, 16, 24, 32}. 96 192 336 512 720 Look-back Length 0.30 0.35 0.40 0.45 MSE ETTm1 96 192 336 720 96 192 336 512 720 Look-back Length 0.15 0.20 0.25 0.30 0.35 MSE weather 96 192 336 720 [PITH_FULL_IMAGE:figures/full_fig_p00…

**Figure 7.** Figure 7: The forecast error of MDMixer with varying look [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: The comparison of training time and memory usage [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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Si-An Chen, Chun-Liang Li, Nate Yoder, Sercan O Arik, and Tomas Pfister. 2023. TSMixer: An all-MLP Architecture for Time Series Forecasting. Transactions on Machine Learning Research (2023)

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