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REVIEW 5 major objections 5 minor 59 references

PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecasting

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

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Pith's one-line read PreMixer: a graph-free all-MLP model with patch-wise MLP pre-training reaches state-of-the-art accuracy on large-scale traffic forecasting.

desk verdict Efficient all-MLP large-scale traffic forecaster with a novel pretraining scheme, but missing key baselines and overblown SOTA claims make the accuracy gains unproven. read the letter →

arxiv 2412.13607 v1 pith:YNS6D7Z3 submitted 2024-12-18 cs.LG cs.ET

Tongtong Zhang , Zhiyong Cui , Bingzhang Wang , Yilong Ren , Haiyang Yu , Pan Deng , Yinhai Wang This is my paper · ORCID
classification cs.LGcs.ET
keywords trafficforecastingMLP-Mixerpre-trainingmaskedautoencodingcontrastivelearningspatio-temporalpositionalencodinglarge-scaledatasetscomputationalefficiency
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 large-scale traffic forecasting can be done accurately and cheaply without graph neural networks or transformers. The proposed framework, PreMixer, couples an MLP-Mixer predictor with a lightweight MLP-based pre-training stage whose patch-wise encoder learns contextual representations from long-term history; it adds spatio-temporal positional encodings and learnable node embeddings in place of a predefined graph. On four real-world datasets with up to 8,600 sensors, the paper reports that PreMixer outperforms twelve baselines on most settings, including the largest dataset, while training roughly an order of magnitude faster than the fastest graph-based competitor. If true, the result matters because deployment-scale traffic forecasting currently struggles with the memory and time demands of graph and attention models.

What carries the argument

The load-bearing object is PIEncoder, a patch-wise MLP autoencoder. Long-term history (one week, 56 patches of length 12) is split into non-overlapping patches; each patch is embedded independently by a two-layer MLP with ReLU, then linearly reconstructed, under a loss that reconstructs both masked and unmasked patches (Equation 3) plus a temporal contrastive loss between two complementary-mask views (Equations 4–5). Patch independence means the encoder shares weights across time and nodes and therefore accepts any input length at forecasting time. The second mechanism is spatio-temporal positional encoding (STPE), which encodes time index and sensor index sinusoidally in separate halves of the feature dimension, together with a learnable node embedding; both are injected into the Mixer predictor to replace a predefined road-network graph.

What would settle it

Run the full PreMixer and its no-pre-training variant multiple times with different random seeds on SD and GBA, then compare MAE distributions; if the 0.37 and 0.33 gaps fall within the run-to-run spread, the pre-training claim collapses. As a second check, pre-train PIEncoder on randomly permuted or time-shuffled patches and retrain the downstream predictor: if accuracy barely changes, the encoder is not contributing real temporal context.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that an all-MLP architecture with two auxiliary components—an MLP-based pre-training encoder and spatio-temporal positional encoding plus learnable node embeddings—can beat established spatiotemporal graph networks and Transformer baselines on large-scale traffic forecasting. The pre-training stage, PIEncoder, embeds each time-series patch independently through a shared two-layer MLP, reconstructs both masked and unmasked patches, and adds a temporal contrastive loss between two views generated by a complementary 50% mask. Because patches never exchange information during pre-training, the learned encoder can process arbitrary input lengths at the forecasting stage, where its representations are projected and added to the Mixer predictor's input. The paper reports the best average MAE/RMSE/MAPE on GBA, GLA, and CA among all compared methods, with the largest gains on the 8,600-sensor CA dataset, and shows that the pre-trained encoder transfers across regions with larger source regions helping more.

Load-bearing premise

The paper's central novelty—that pre-training on long-term patches is what gives PreMixer its edge—rests on an ablation on two datasets (SD and GBA) with no error bars or significance tests, so the small MAE gaps (0.37 and 0.33) could be run-to-run noise.

Editorial extensions

If this is right

  • Large-scale deployment becomes practical: PreMixer trains and infers far faster than every baseline, and it is one of only a few models that runs on the largest 8,600-sensor dataset at all.
  • The pre-trained patch encoder can be reused across regions: transferring from the large CA dataset improves downstream results on SD, while transfers from smaller or differently distributed regions do not.
  • Each component contributes: removing pre-training, contrastive learning, context, or STPE degrades MAE on SD and GBA, so the full composition is what achieves the reported accuracy.
  • The architecture's success on the two largest datasets suggests that graph structure is not necessary for capturing spatial dependencies in large-scale traffic networks.

Reading between the lines

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

  • Because patch embeddings are independent and input-agnostic, the same pre-train-and-mix recipe could be dropped into other multivariate spatiotemporal forecasting problems—energy load, weather station networks, or city-wide demand—where weekly periodicity and sensor heterogeneity matter but no reliable graph exists.
  • The pre-training benefit is the least certain part of the claim: the only direct evidence is a two-dataset ablation with small MAE gaps and no error bars, so multi-seed runs are needed before the pre-training stage can be credited rather than the Mixer backbone or STPE.
  • The unusually high RMSE values reported for TSMixer on GLA and CA suggest that the plain MLP-Mixer baseline becomes numerically unstable at scale; if so, part of PreMixer's advantage may come from auxiliary embeddings that stabilize mixing, which would be worth isolating experimentally.
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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

5 major / 5 minor

Summary. The paper proposes PreMixer, an all-MLP framework for large-scale traffic forecasting that combines a patch-wise MLP autoencoder pre-training stage with a downstream MLP-Mixer predictor. The pre-training uses masked reconstruction and complementary contrastive learning on long-term history, while the downstream model uses spatio-temporal positional encoding and learnable node embeddings to avoid graph dependence. Experiments on four LargeST sub-datasets (SD, GBA, GLA, CA) report competitive MAE/RMSE/MAPE with substantially lower training and inference time than graph-based baselines.

Significance. If the empirical claims hold, PreMixer offers a graph-free, efficient alternative for large-scale traffic forecasting, with pre-training enhancing downstream accuracy at low computational cost. The efficiency gains reported in Table V are striking (e.g., about 4 hours total training on CA versus 84-207 hours for some baselines), and the patch-wise independent encoding idea is simple and potentially transferable. However, the significance is tempered by the absence of the most closely related MLP-Mixer and pre-training baselines, by the lack of statistical validation for the small pre-training gains, and by the overstatement that PreMixer outperforms all state-of-the-art methods.

major comments (5)
  1. [§IV-B, Table II] The claim that 'PreMixer outperforms state-of-the-art methods' (Section I, contribution 4) is not supported by the reported numbers: on SD the average MAE of D2STGNN (17.38) and DGCRN (17.65) are both lower than PreMixer's 18.02, and on GBA TSMixer's average MAE (19.58) is lower than PreMixer's 20.06. PreMixer is best only on the two largest datasets, GLA and CA. This overstatement should be corrected, for example by describing the results as 'competitive' or 'best on the two largest datasets'.
  2. [§IV-A2 and Table II] The paper does not compare against any MLP-Mixer-based traffic baselines (NexuSQN [37], STID [28], ST-MLP [36], RPMixer [35]) or pre-training baselines (STEP [27], STD-MAE [31]), despite citing them in the literature review. Section III-B explicitly adapts the pattern-aware mixing operation from NexuSQN and fuses spatio-temporal positional encoding with learnable node embeddings, which closely resembles NexuSQN's spatio-temporal node embedding. As a result, the ablation 'w/o Pre-training' (Table IV) isolates the pre-training contribution only relative to PreMixer itself, not relative to the architecture it is built upon; a comparison with NexuSQN is needed to support both the novelty and accuracy claims.
  3. [§IV-D, Table IV] The downstream improvement from pre-training is reported as a MAE decrease of 0.37 on SD and 0.33 on GBA, with no error bars or significance tests. Given the typical variance across random seeds in traffic forecasting experiments, these differences may be within run-to-run noise. The authors should report mean and standard deviation over multiple runs and provide a statistical test, at least for the ablations of the two key components (pre-training and contrastive learning), to substantiate the central claim that pre-training helps.
  4. [§IV-E, Table V] The efficiency analysis omits the cost of the pre-training stage. Table V reports per-epoch training and inference times for the forecasting model, but the total training time should also include the pre-training phase on long-term historical data; otherwise the claim of 'without incurring significant time consumption' is not fully substantiated. Additionally, the TSMixer RMSE values on GLA and CA (e.g., 224.82 at horizon 3 on GLA, 106.28 at horizon 3 on CA) are orders of magnitude larger than the corresponding MAE values (20.38 and 18.40), which suggests a bug or misconfiguration in the baseline; this undermines the fairness of the comparison on those datasets.
  5. [§III-B1, Eqs. (4)-(5)] The contrastive learning formulation is unclear and likely misindexed: the text 'Assume z(i,n)1 = z(i+Tp,n)1 and z(i+2Tp,n)1 be the two views' is confusing, and Eq. (4) sums over 2Tp items while the original patched input has Tp patches. Please rewrite the two-view generation and the positive-pair indexing precisely, and clarify why both masked and unmasked patches are reconstructed in the reconstruction loss.
minor comments (5)
  1. [Throughout] The manuscript contains numerous typos and grammatical errors, such as 'sptiotemporal', 'rode networks', 'designes', 'imporvement', 'trining', and 'conducted'. A careful language revision is needed.
  2. [§III-B, Eq. (7)] The spatio-temporal positional encoding formula uses both C and D inconsistently; the dimensions of Upos should be defined clearly and the indexing in Eq. (7) should be consistent with the stated shape R^{T x N x C}.
  3. [§II-B, reference [53]] Reference [53] is a paper on translating math formula images, not an appropriate source for sinusoidal positional encoding; the original Transformer paper (Vaswani et al., 2017) should be cited instead.
  4. [§IV-A2, baselines] The baseline list omits the recent MLP-Mixer and pre-training baselines discussed in the literature review; at minimum, the authors should state why these methods were excluded, or add them to Table II.
  5. [§IV-D] The sentence 'The PreMixer, equipped with auxiliary information, significantly outperforms its ablated versions' is an overstatement given the small differences in Table IV and the absence of significance tests; the wording should be softened.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation found: PreMixer's pretraining and forecasting stages are independently specified, and the claimed gains are tested by ablation against held-out data rather than being forced by construction.

full rationale

On inspection, the paper's derivation chain is self-contained rather than circular. The pretraining stage trains PIEncoder with a patch reconstruction loss and a temporal contrastive loss (Eqs. 3 and 5) on long-term historical patches; the forecasting stage is an independent supervised MLP-Mixer-style model (Eqs. 8-13) evaluated on held-out test splits of the LargeST benchmark. The effect of pretraining is tested by an ablation that removes the pretraining module (Table IV), so the reported improvement is an empirical claim, not an identity. The SpatialMixer adapts pattern-aware mixing from NexuSQN [37], an external prior work, and the STPE/learnable node embedding are presented as fusions of standard sinusoidal embeddings with trainable node features; neither is derived from a self-citation or fitted to the target result. The authors' own earlier works [6], [7] are cited only as background deep-learning references for traffic forecasting and are not load-bearing in the derivation. Finally, the absence of close MLP-Mixer baselines (e.g., NexuSQN, STID, ST-MLP) in Table II is a legitimate evaluation-completeness concern, but it is not a circularity: the paper does not define its prediction target in terms of those baselines, nor does it fit a parameter to the test set.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The model depends on standard ML assumptions and a set of hand-chosen hyperparameters. The main burden is the assumption that frozen patch-wise MLP representations transfer to a different downstream predictor, which is tested only weakly. No new physical or formal entities are introduced.

free parameters (7)
  • mask_ratio = 0.5
    Masking ratio for complementary views in pretraining; set to 50% without sensitivity analysis (Section III-B.1).
  • patch_length = 12
    Each patch is 12 time steps; 56 patches cover one week of historical data (Section IV-A).
  • pretraining_hidden_dim = 96
    Latent dimension D of PIEncoder representations (Section IV-A).
  • learning_rate = 0.005
    Adam learning rate in the forecasting stage (Section IV-A).
  • batch_size = 32
    Batch size in the forecasting stage (Section IV-A).
  • mixer_depth_L
    Number of TemporalMixer/SpatialMixer layers L in Equations 10-12 is not reported in the paper.
  • node_embedding_dim
    Dimension of the learnable node embedding dictionary E is not stated in the methodology or experiments.
assumptions (5)
  • domain assumption LargeST 2019 data at 15-minute resolution is representative of large-scale traffic forecasting.
    The paper trains and tests only on 2019 PeMS data from LargeST and assumes the resulting conclusions transfer to other large-scale networks.
  • domain assumption Reconstruction and temporal contrastive losses on traffic patches produce transferable contextual representations.
    The pretraining contribution depends on the assumption that frozen patch-wise MLP embeddings improve a different downstream predictor, which is tested only weakly in Section IV-D.
  • domain assumption Baseline implementations and hyperparameters are correct and comparable.
    The paper follows the LargeST experimental framework, but no tuning details or error bars are provided for the baselines, and TSMixer shows anomalous RMSE values on large datasets.
  • ad hoc to paper Sinusoidal spatio-temporal positional encoding resolves sample indistinguishability without a graph.
    The paper postulates that Equation 7 provides useful positional context for the MLP-Mixer, but the encoding has an indexing inconsistency between C and D and is not independently justified.
  • standard math Standard gradient-based optimization with Adam and an MAE regression loss is sufficient to train the framework.
    The paper relies on conventional deep learning optimization assumptions without analysis of convergence.

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Cite this review

Pith. "Pith review of PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecasting." pith.science (2026). https://pith.science/paper/YNS6D7Z3

@misc{pith2026241213607,
  author       = {Pith},
  title        = {Pith review of: PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YNS6D7Z3}},
  note         = {Machine review of arXiv:2412.13607}
}
read the original abstract

In urban computing, precise and swift forecasting of multivariate time series data from traffic networks is crucial. This data incorporates additional spatial contexts such as sensor placements and road network layouts, and exhibits complex temporal patterns that amplify challenges for predictive learning in traffic management, smart mobility demand, and urban planning. Consequently, there is an increasing need to forecast traffic flow across broader geographic regions and for higher temporal coverage. However, current research encounters limitations because of the inherent inefficiency of model and their unsuitability for large-scale traffic network applications due to model complexity. This paper proposes a novel framework, named PreMixer, designed to bridge this gap. It features a predictive model and a pre-training mechanism, both based on the principles of Multi-Layer Perceptrons (MLP). The PreMixer comprehensively consider temporal dependencies of traffic patterns in different time windows and processes the spatial dynamics as well. Additionally, we integrate spatio-temporal positional encoding to manage spatiotemporal heterogeneity without relying on predefined graphs. Furthermore, our innovative pre-training model uses a simple patch-wise MLP to conduct masked time series modeling, learning from long-term historical data segmented into patches to generate enriched contextual representations. This approach enhances the downstream forecasting model without incurring significant time consumption or computational resource demands owing to improved learning efficiency and data handling flexibility. Our framework achieves comparable state-of-the-art performance while maintaining high computational efficiency, as verified by extensive experiments on large-scale traffic datasets.

Figures

Figures reproduced from arXiv: 2412.13607 by the authors.

Figure 1
Figure 1. A comprehensive comparison with recent methods [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overall schematic of the PreMixer. with contextual information, enhancing the downstream pre￾diction. The details of these processes are elaborated in the following two subsections. 1) The Pre-training Stage: In standard traffic forecasting tasks, the input typically contains short-term historical time series data, and the model struggles to capture long-term temporal patterns, resulting in lower prediction performa… view at source ↗
Figure 3
Figure 3. The Pre-training Stage. Left: the overview of the proposed PIEncoder. We segment prolonged time series data spanning [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: An illustration of the LargeST benchmark dataset [ [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Comparison of PreMixer with baseline models across [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 7
Figure 7. Figure 7: Comparison of the ground truth and the flow predicted by PreMixer tested on the LargeST dataset. The three sub-figures [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

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