MCST-Mamba: Multivariate Mamba-Based Model for Traffic Prediction

Mohamed Hamad; Mohamed Mabrok; Nizar Zorba

REVIEW 3 major objections 5 minor 14 references

MCST-Mamba: Multivariate Mamba-Based Model for Traffic Prediction

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read MCST-Mamba claims state-of-the-art MAE and RMSE on PEMS04 and PEMS08 by jointly predicting speed, flow, and occupancy with 0.49M parameters.

desk verdict Plausible Mamba-based multi-channel architecture, but the SOTA claim rests on comparing aggregated three-channel errors with speed-only baselines, so the headline result is unsupported. read the letter →

arxiv 2507.03927 v1 pith:F5B4HW2L submitted 2025-07-05 cs.LG

Mohamed Hamad , Mohamed Mabrok , Nizar Zorba This is my paper · ORCID

classification cs.LG

keywords trafficpredictionmultivariatetimeseriesMambaselectivestatespacemodelspatio-temporalforecastingmulti-channelPEMS04/PEMS08parameterefficiency

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

MCST-Mamba is a traffic forecasting model built on the Mamba selective state-space architecture, designed to predict speed, flow, and occupancy for every sensor at the same time instead of forecasting one variable or training a separate model per channel. The paper argues that treating all three measurements as one multivariate sequence lets Mamba capture inter-channel dependencies that single-channel models miss, and that splitting sequence modeling into a temporal Mamba block and a spatial Mamba block captures the two kinds of structure without requiring a predefined road graph. On PEMS04 and PEMS08, the model reports MAE of 7.88 and 6.54 and RMSE of 20.97 and 16.43, respectively, with only 0.49M parameters. The paper's stated contribution is that a compact model can jointly handle three times the output dimensionality of typical baselines while still beating their reported single-channel speed errors.

What carries the argument

The central object is the MCST-Mamba block, a selective state-space model with normalization, residual connections, and a feed-forward layer, applied in two pathways. The temporal pathway reshapes the input to [n, m·t, f], so each sensor's multivariate series is one sequence; the spatial pathway reshapes to [t, m·n, f], so each time step is a network-wide snapshot; the two pathway outputs are combined by learnable scalar weights. Before the blocks, four embeddings are concatenated: a 24-dimensional feature embedding, time-of-day and day-of-week table embeddings, a 16-dimensional learnable spatial embedding per node, and an 80-dimensional adaptive spatio-temporal embedding, all projected into Mamba's 96-dimensional internal space. This machinery is what lets the model avoid explicit graph construction while still modeling spatial interaction.

What would settle it

Re-run STAEformer or ST-Mamba on the same task of predicting all three channels and compute the same aggregated MAE and RMSE; if their aggregated errors reach or fall below MCST-Mamba's 7.88 and 20.97 on PEMS04 and 6.54 and 16.43 on PEMS08, the claimed state-of-the-art result is not supported.

Watch

Extended reading notes

Core claim

The paper's central claim is that a Mamba-based forecaster can natively process and predict all three traffic channels together and achieve lower MAE and RMSE than specialized graph, transformer, and state-space baselines while using about 0.49M parameters. To do this, MCST-Mamba feeds the raw four-dimensional sensor tensor through feature, time-of-day/day-of-week, spatial, and adaptive embeddings, then runs two separate Mamba blocks: one that treats each sensor's multivariate history as a sequence, and one that treats each time step as a spatial snapshot across sensors. The two outputs are weighted by learnable scalars and projected to the prediction. The paper also claims that evaluating all channels simultaneously is the more realistic protocol for congestion, because congestion is a joint effect of speed, flow, and occupancy rather than a single-variable phenomenon.

Load-bearing premise

The central claim assumes that an error aggregated over speed, flow, and occupancy is directly comparable to published baselines' speed-only errors, even though the three variables have different units and scales.

Editorial extensions

If this is right

A single 0.49M-parameter model can output speed, flow, and occupancy for an entire sensor network in one forward pass, replacing per-variable model stacks.
No road graph is required during training or inference, so the model can be applied to a new sensor network without graph construction or adjacency tuning.
The reported parameter count suggests the multivariate Mamba backbone is cheap enough for deployment on resource-constrained traffic controllers.
The dual temporal and spatial pathways give a template for injecting structure into Mamba beyond traffic, wherever data is a tensor over locations and time.
If the results hold under per-channel evaluation, the practice of benchmarking only speed should shift to multi-channel metrics.

Reading between the lines

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

The headline comparison mixes levels: baseline numbers are speed-only while MCST-Mamba's are averaged over speed, flow, and occupancy, which have different units and scales; a fair test would re-run baselines on all three channels under the same aggregate metric.
A natural falsifying experiment is to replace MCST-Mamba's three-channel output with speed-only output and compare directly to the published baseline speed numbers, which would isolate whether the reported gains come from the architecture or from the evaluation protocol.
The same dual-pathway reshaping could be applied to other multivariate spatiotemporal datasets such as energy grids or environmental sensor networks, with the learnable scalar integration offering a cheap way to tune the space-versus-time emphasis for each dataset.

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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

The paper builds a sensible Mamba-based model that predicts speed, flow, and occupancy jointly, using STAEformer-style adaptive embeddings and two separate Mamba blocks for temporal and spatial pathways. That architecture is a legitimate incremental combination of known ideas, and the parameter count is modest. The writing is clear, the code is public, and the authors are transparent about the evaluation mismatch. So there is a real kernel here, but the empirical case is not made.

The load-bearing problem is Table II. As the paper itself states in Section IV-F.1, the baseline numbers are single-channel speed metrics from the STAEformer paper, while MCST-Mamba's metrics are aggregated over speed, flow, and occupancy. MAE and RMSE are scale-dependent; pooling three channels with different units and ranges makes the comparison meaningless. The MAPE, which is scale-invariant, is worse for MCST-Mamba on both datasets (16.05% vs. 11.88% on PEMS04; 12.06% vs. 8.80% on PEMS08). So the claimed state-of-the-art performance rests entirely on a broken comparison. The stress-test note is right, and I don't see any way to rescue the headline claim as stated.

The paper also lacks per-channel breakdowns, matched multi-channel baselines, and repeated-run error bars. The parameter-efficiency argument is suggestive but not properly benchmarked against a multi-channel model of similar size. These are fixable omissions, but they are not minor: without like-for-like evaluation, the central contribution is unverified.

What the paper does well is frame a real problem—many traffic models ignore the multivariate structure or train separate models per channel. The dual-pathway Mamba design is reasonable, and the authors are honest about the mismatch and about their MAPE being worse. That honesty counts, but it doesn't turn an invalid comparison into a valid one.

For whom is this paper? Someone working on Mamba-based time series or multivariate traffic forecasting might find the architecture worth a look, but they should not cite the empirical claims. I would not use the reported numbers in my own work.

My recommendation: send it to peer review, but only with a strong request for major revision. The authors need to run matched baselines that predict all three channels, report per-channel metrics, and provide error bars. If the model survives that test, it is a modest but real contribution. If not, the paper should not be published on its current evidence.

Referee Report

3 major / 5 minor

Summary. The paper proposes MCST-Mamba, a dual-pathway selective state-space model for multivariate traffic forecasting that predicts speed, flow, and occupancy simultaneously on the PEMS04 and PEMS08 datasets. The architecture combines STAEformer-style feature, temporal, spatial, and adaptive embeddings with separate Mamba blocks for temporal and spatial dependencies, whose outputs are combined with learned scalar weights. The authors report strong MAE and RMSE numbers with 0.49M parameters and argue that this demonstrates state-of-the-art performance while being parameter-efficient relative to single-channel baselines.

Significance. Multivariate traffic prediction is practically relevant, and the paper addresses a genuine limitation of many existing models that only forecast one traffic variable. The architectural idea of using separate temporal and spatial Mamba pathways on the native multivariate input is reasonable, and the authors have released code, which is a strength. If the reported comparison were valid, a 0.49M-parameter model predicting all three channels would be a useful contribution. However, the central empirical claim is not established as written because the baseline metrics are not comparable to the reported MCST-Mamba metrics.

major comments (3)

[Section IV-F.1, Table II] The headline state-of-the-art claim is based on comparing speed-only baseline MAE/RMSE values with MCST-Mamba MAE/RMSE values aggregated over speed, flow, and occupancy. MAE and RMSE are scale-dependent, and the three traffic channels have different physical units and ranges, so a lower pooled error does not imply better forecasting performance on any individual channel, let alone on the same task as the baselines. The paper explicitly acknowledges this mismatch in Section IV-F.1, yet still claims state-of-the-art performance. To support the claim, the authors need to provide either matched multi-channel baselines or per-channel speed-only metrics for MCST-Mamba.
[Section IV-F.1, Table II] The only scale-invariant metric reported, MAPE, is worse for MCST-Mamba than for several baselines on both datasets: 16.05% versus 11.88% for ST-Mamba on PEMS04, and 12.06% versus 8.80% for ST-MambaSync on PEMS08. Because MAPE is not affected by the multi-channel pooling in the same way as MAE/RMSE, this directly contradicts the overall superiority claim and requires a per-channel MAPE breakdown and explanation.
[Section IV-F.1] No per-channel breakdown and no repeated-run error bars are reported. Given the stochasticity of neural network training, single-run numbers are insufficient to support a claim of state-of-the-art performance, especially when the comparison is not apples-to-apples. The authors should report per-channel MAE, RMSE, and MAPE for MCST-Mamba and, ideally, confidence intervals from multiple seeds, so that readers can assess which of the three outputs drives the pooled result.

minor comments (5)

[Section II-B and Section III-A] Equation (4) in Related Work defines Z as Ef || Ep || Ea, while Equation (6) in the methodology includes E_spatial as an additional component; the notation should be made consistent, and the projection dimensions in Equation (7) should be checked for consistency with the stated embedding dimensions.
[Section IV-A, Figure 1] Figure 1 contains the typo 'Spacial', which should be 'Spatial'.
[Abstract and Section I] There are minor typos such as 'simulataneously' and inconsistent dataset naming between 'PEMS-D4/PEMS-D8' in Section IV-B and 'PEMS04/PEMS08' in Table II; the names should be unified.
[Section IV-E] The paper does not state the number of random seeds or repeated runs used to produce the reported metrics; this should be specified.
[Section IV-F.2] The parameter-efficiency argument compares MCST-Mamba with single-channel baselines, but the meaningful comparison for a multi-channel model is against multi-channel baselines or against single-channel models evaluated on the same output scope; this should be clarified.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: MCST-Mamba is benchmarked on external test data, and the Table II mismatch between pooled three-channel and speed-only baselines is a soundness issue, not a construction-by-input.

full rationale

The central claim of the paper is empirical rather than derivational: MCST-Mamba is trained and evaluated on external benchmarks (PEMS-D4, PEMS-D8), the implementation is released, and its reported MAE, RMSE, and MAPE are test-set quantities computed from held-out data, not functions of the baseline numbers. No parameter is fitted to the baselines, and no uniqueness theorem or ansatz is imported from the authors' own prior work; the STAEformer-style adaptive embedding is adopted from external work [6] and explicitly modified (Eq. 6 adds a spatial embedding). The one flag-worthy passage is Section IV-F.1, which states that 'the metrics reflect performance on a single predicted channel (speed). In contrast, the metrics for MCST-Mamba represent the aggregated error across all three predicted channels,' and Section IV-F.2 repeats the single-channel caveat. This protocol mismatch means the claimed state-of-the-art status in Table II is unsupported because the comparison is not like-for-like; however, that is a correctness or soundness problem, not circularity, since the MCST-Mamba numbers are not defined in terms of the baseline numbers and do not reduce to them by construction. Corroborating the absence of circularity, the paper openly reports losing on MAPE against baselines (16.05% vs. 11.88% on PEMS04; 12.06% vs. 8.80% on PEMS08), which is inconsistent with a narrative whose metrics are manufactured to guarantee victory. Self-citations [2], [3], and [5] include co-authors Zorba and Mabrok, but they are background context citations (external factors, sensor networks, general deep-learning advances) and bear no load for the central result. Verdict: no significant circularity, with a noted evaluation-protocol limitation that should be weighed as a support, not a tautology, concern.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

No physical constants or ad hoc theoretical parameters are introduced. The central claim depends on hand-selected hyperparameters and on the comparability assumption described in the axioms. The model introduces no new entities, forces, or conserved quantities.

free parameters (9)

Embedding dimensions (D_input, D_tod, D_dow, D_spatial, D_adaptive) = 24, 24, 24, 16, 80
Chosen by hand; no ablation shows sensitivity to these values.
Mamba internal dimension D_mamba = 96
Chosen by hand; no ablation reported.
SSM state dimension N = 32
Chosen by hand; no ablation reported.
Expansion factor = 2
Chosen by hand; no ablation reported.
Dropout rate = 0.1
Chosen by hand; no sensitivity analysis reported.
Initial learning rate (Adam) = 0.001
Standard value; no tuning or sensitivity analysis reported.
Batch size = 64
Chosen by hand; no sensitivity analysis reported.
Early stopping patience = 15
Chosen by hand; no sensitivity analysis reported.
Mamba blocks per pathway = 1
Chosen by hand; no ablation on block count reported.

assumptions (5)

domain assumption The Mamba selective state space model correctly models long-range temporal dependencies in traffic time series.
Taken from citations [7], [10], [11] without independent verification in this paper.
domain assumption The STAEformer adaptive embedding E_a captures spatio-temporal structure that transfers successfully to Mamba blocks.
Adopted from [6]; no ablation isolates its contribution in this architecture.
domain assumption Speed, flow, and occupancy jointly describe congested traffic, and joint modeling improves prediction.
Stated in Sections I and III but not separately validated in the experiments.
ad hoc to paper Aggregated MAE/RMSE over speed, flow, and occupancy is comparable to published single-channel speed error.
Used in Table II and Section IV-F.1; this is the load-bearing comparison assumption and is not justified.
domain assumption The 70/10/20 data split and z-score normalization match the setup used to generate the imported baseline numbers.
Standard practice, but baseline numbers are imported from the STAEformer paper [6] and preprocessing may differ.

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Cite this review

Pith. "Pith review of MCST-Mamba: Multivariate Mamba-Based Model for Traffic Prediction." pith.science (2026). https://pith.science/paper/F5B4HW2L

@misc{pith2026250703927,
  author       = {Pith},
  title        = {Pith review of: MCST-Mamba: Multivariate Mamba-Based Model for Traffic Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F5B4HW2L}},
  note         = {Machine review of arXiv:2507.03927}
}

read the original abstract

Accurate traffic prediction plays a vital role in intelligent transportation systems by enabling efficient routing, congestion mitigation, and proactive traffic control. However, forecasting is challenging due to the combined effects of dynamic road conditions, varying traffic patterns across different locations, and external influences such as weather and accidents. Traffic data often consists of several interrelated measurements - such as speed, flow and occupancy - yet many deep-learning approaches either predict only one of these variables or require a separate model for each. This limits their ability to capture joint patterns across channels. To address this, we introduce the Multi-Channel Spatio-Temporal (MCST) Mamba model, a forecasting framework built on the Mamba selective state-space architecture that natively handles multivariate inputs and simultaneously models all traffic features. The proposed MCST-Mamba model integrates adaptive spatio-temporal embeddings and separates the modeling of temporal sequences and spatial sensor interactions into two dedicated Mamba blocks, improving representation learning. Unlike prior methods that evaluate on a single channel, we assess MCST-Mamba across all traffic features at once, aligning more closely with how congestion arises in practice. Our results show that MCST-Mamba achieves strong predictive performance with a lower parameter count compared to baseline models.

Figures

Figures reproduced from arXiv: 2507.03927 by the authors.

**Figure 1.** MCST-Mamba Architecture A. Embeddings and Data Preparation In our model, we transform the raw traffic data into a rich representation space through multiple embedding strategies adopted from the STAEformer architecture. The embedding process captures temporal patterns and spatial characteristics, providing the model with comprehensive context. Given the input tensor X ∈ R m×tin×n×f , we construct the final multi-com… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 8 canonical work pages

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Deep learning on traffic prediction: Methods, analysis, and future directions,

X. Yin, G. Wu, J. Wei, Y . Shen, H. Qi, and B. Yin, “Deep learning on traffic prediction: Methods, analysis, and future directions,”IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 6, pp. 4927–4943, 2022

2022

[2] [2]

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A. Ramadan, A. Elbery, N. Zorba, and H. S. Hassanein, “Traffic fore- casting using temporal line graph convolutional network: Case study,” inICC 2020 - 2020 IEEE International Conference on Communications (ICC), 2020, pp. 1–6

work page 2020

[3] [3]

idrivesense: Dynamic route planning involving roads quality infor- mation,

A. S. El-Wakeel, A. Noureldin, H. S. Hassanein, and N. Zorba, “idrivesense: Dynamic route planning involving roads quality infor- mation,” in2018 IEEE Global Communications Conference (GLOBE- COM), 2018, pp. 1–6

work page 2018

[4] [4]

A task-oriented spatial graph structure learning method for traffic forecasting,

T. Wang, S. Zhao, W. Jia, and D. Shi, “A task-oriented spatial graph structure learning method for traffic forecasting,”IEEE Transactions on Intelligent Transportation Systems, vol. 26, no. 4, pp. 4770–4779, 2025

work page 2025

[5] [5]

An online learning framework for uav target search missions in non-stationary environments,

N. Khial, N. Mhaisen, M. Mabrok, and A. Mohamed, “An online learning framework for uav target search missions in non-stationary environments,” in2024 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 2024, pp. 753–758

work page 2024

[6] [6]

Frugal Prompting for Dialog Models

X. Liu, J. Zhou, Y . Zheng, M. Xu, Y . Liu, H. Zhang, M. Jiang, and Z. Li, “Staeformer: Spatio-temporal adaptive embedding transformer for traffic forecasting,”arXiv preprint arXiv:2305.14919, 2023

work page Pith review arXiv 2023

[7] [7]

Mamba: Linear- time sequence modeling with selective state spaces,

A. Gu, T. Dao, S. Ermon, A. Rudra, and C. R ´e, “Mamba: Linear- time sequence modeling with selective state spaces,”arXiv preprint arXiv:2312.00752, 2023

arXiv 2023

[8] [8]

Semi-mamba: Mamba- driven semi-supervised multimodal remote sensing feature classifica- tion,

Y . Li, D. Li, W. Xie, J. Ma, S. He, and L. Fang, “Semi-mamba: Mamba- driven semi-supervised multimodal remote sensing feature classifica- tion,”IEEE Transactions on Circuits and Systems for Video Technology, pp. 1–1, 2025

work page 2025