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arxiv: 2604.09336 · v1 · submitted 2026-04-10 · 💻 cs.LG

Hierarchical Flow Decomposition for Turning Movement Prediction at Signalized Intersections

Md Atiqur Rahman Mallick , Kamrul Hasan , Pulock Das , Liang Hong , S M Shazzad Rassel This is my paper

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification 💻 cs.LG
keywords turning movement predictionhierarchical decompositiontraffic flow forecastingdeep learningflow conservationsignalized intersectionsadaptive signal control
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The pith

Predicting vehicle turns at traffic lights improves when stable corridor flows are forecasted first and then split into specific turns.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to demonstrate that breaking the prediction task into two levels, first estimating the more stable corridor through movements and then allocating those to individual turning streams, yields more accurate results for volatile turning flows at intersections. A reader would care because reliable turning predictions support adaptive traffic signals that can adjust timing to cut delays and congestion. The design rests on observed patterns where corridor flows make up the bulk of volume, fluctuate less, and account for a sizable share of turning variation. A loss term that enforces conservation of total flow keeps the decomposed predictions physically consistent. Tests on six months of sensor data from a Nashville corridor show the approach outperforms standard recurrent and attention-based models while training much faster.

Core claim

HFD-TM forecasts turning movements by first predicting corridor through-movements and then expanding those forecasts to the individual turning streams at each intersection, with a physics-informed loss that enforces flow conservation across the hierarchy.

What carries the argument

Hierarchical decomposition that separates corridor-level forecasting from turning-movement expansion, guided by a physics-informed loss enforcing flow conservation.

If this is right

  • The hierarchical approach accounts for the largest share of the observed accuracy gain over direct forecasting methods.
  • Predictions maintain consistency with total observed flows due to the conservation constraint.
  • Training completes substantially faster than comparable graph-based recurrent models, supporting real-time use.
  • The two-stage structure reduces error on volatile turning movements by leveraging the stability of corridor flows.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same volume and volatility patterns appear in other cities, the decomposition structure could be reused without redesigning the model architecture.
  • The separation of stable aggregate flows from variable components may extend to forecasting tasks in other domains with similar hierarchical structure.
  • Adaptive signal systems could incorporate these forecasts to allocate green time more precisely across turning movements.

Load-bearing premise

The traffic volume split and volatility differences observed in one Nashville corridor apply to other intersections and times.

What would settle it

A new dataset from a different corridor where the hierarchical model shows no accuracy improvement over direct prediction baselines would falsify the claimed benefit.

Figures

Figures reproduced from arXiv: 2604.09336 by Kamrul Hasan, Liang Hong, Md Atiqur Rahman Mallick, Pulock Das, S M Shazzad Rassel.

Figure 1
Figure 1. Figure 1: System-level overview of the proposed HFD-TM framework. Block A encodes corridor [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of mean absolute error (MAE) across baseline models and the proposed [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

Accurate prediction of intersection turning movements is essential for adaptive signal control but remains difficult due to the high volatility of directional flows. This study proposes HFD-TM (Hierarchical Flow-Decomposition for Turning Movement Prediction), a hierarchical deep learning framework that predicts turning movements by first forecasting corridor through-movements and then expanding these predictions to individual turning streams. This design is motivated by empirical traffic structure, where corridor flows account for 65.1% of total volume, exhibit lower volatility than turning movements, and explain 35.5% of turning-movement variance. A physics-informed loss function enforces flow conservation to maintain structural consistency. Evaluated on six months of 15-minute interval LiDAR (Light Detection and Ranging) data from a six-intersection corridor in Nashville, Tennessee, HFD-TM achieves a mean absolute error of 2.49 vehicles per interval, reducing MAE by 5.7% compared to a Transformer and by 27.0% compared to a GRU (Gated Recurrent Unit). Ablation results show that hierarchical decomposition provides the largest performance gain, while training time is 12.8 times lower than DCRNN (Diffusion Convolutional Recurrent Neural Network), demonstrating suitability for real-time traffic applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The paper introduces HFD-TM, a hierarchical deep learning model for predicting turning movements at signalized intersections. It first forecasts corridor through-movements (motivated by empirical observations that these account for 65.1% of volume and explain 35.5% of turning variance with lower volatility) and then expands them to individual turning streams via a decomposition step, augmented by a physics-informed loss enforcing flow conservation. Evaluated on six months of 15-minute LiDAR data from a six-intersection Nashville corridor, the model reports MAE of 2.49 vehicles/interval, with 5.7% improvement over a Transformer baseline, 27.0% over GRU, largest gains from the hierarchical component in ablations, and 12.8x faster training than DCRNN.

Significance. If the performance gains and efficiency hold under broader conditions, the work offers a practical advance for real-time adaptive signal control by exploiting traffic structure to reduce volatility in predictions. The explicit ablation isolating the hierarchical decomposition benefit and the physics-informed constraint are strengths that could guide similar structured models in transportation ML. However, the single-corridor evaluation limits claims of general suitability for real-time applications.

major comments (3)
  1. [§2 and §4] §2 (Motivation) and §4 (Experiments): The corridor-flow statistics (65.1% volume, 35.5% variance explained) are presented as motivation for the fixed hierarchical structure, yet all results—including ablations and baseline comparisons—are confined to the same Nashville dataset without reporting whether these percentages were computed solely on the training split or the full corpus. This leaves open whether the design choice introduces data-dependent bias when the model is deployed elsewhere.
  2. [§5] §5 (Discussion/Conclusion): The claim that HFD-TM demonstrates suitability for real-time traffic applications rests on the transferability of the Nashville-derived decomposition (corridor flows first, then expansion). No cross-location, cross-city, or temporal-shift experiments are reported to test whether the 65.1%/35.5% structure or the observed MAE gains persist when flow proportions or volatility differ, which is load-bearing for the central attribution of gains to the hierarchical design.
  3. [§4] §4 (Results): While concrete MAE, percentage improvements, and ablation deltas are reported, the manuscript does not include error bars, statistical significance tests across multiple random seeds, or details on the exact train/validation/test split ratios and temporal blocking for the 6-month 15-min intervals. This weakens confidence that the 5.7% and 27.0% gains are robust rather than sensitive to a particular held-out interval.
minor comments (3)
  1. [Figure 3] Figure 3 (or equivalent architecture diagram): The expansion step from corridor predictions to turning streams should explicitly label the learned vs. fixed parameters to clarify how much of the hierarchy is data-driven versus hand-specified from the Nashville statistics.
  2. [§3] §3 (Method): The physics-informed loss is described qualitatively; adding the exact mathematical form (e.g., the conservation penalty term) would allow readers to assess its weighting relative to the primary MAE objective.
  3. [Table 2] Table 2 (baseline comparison): Include the number of parameters and inference latency for all models (Transformer, GRU, DCRNN, HFD-TM) to substantiate the training-time advantage claim beyond the single 12.8x factor.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below, indicating where revisions will be incorporated to improve the manuscript.

read point-by-point responses

  1. Referee: [§2 and §4] §2 (Motivation) and §4 (Experiments): The corridor-flow statistics (65.1% volume, 35.5% variance explained) are presented as motivation for the fixed hierarchical structure, yet all results—including ablations and baseline comparisons—are confined to the same Nashville dataset without reporting whether these percentages were computed solely on the training split or the full corpus. This leaves open whether the design choice introduces data-dependent bias when the model is deployed elsewhere.

    Authors: The 65.1% and 35.5% figures were computed on the full six-month corpus solely to motivate the hierarchical design based on observed corridor-level structure. To address the concern about potential bias, the revised manuscript will explicitly state this computation detail and include a new supplementary table recomputing the same statistics on the training split only. This will confirm that the motivation holds under training-data-only conditions and clarify that the fixed structure is not derived from test data. revision: yes

  2. Referee: [§5] §5 (Discussion/Conclusion): The claim that HFD-TM demonstrates suitability for real-time traffic applications rests on the transferability of the Nashville-derived decomposition (corridor flows first, then expansion). No cross-location, cross-city, or temporal-shift experiments are reported to test whether the 65.1%/35.5% structure or the observed MAE gains persist when flow proportions or volatility differ, which is load-bearing for the central attribution of gains to the hierarchical design.

    Authors: We agree that transferability is central to broader claims. The current work is presented as a case study on one corridor; the revised discussion and conclusion will be updated to avoid overgeneralizing suitability for real-time applications and will instead emphasize that the hierarchical decomposition exploits a common traffic pattern that can be recomputed per site. A new limitations paragraph will be added outlining the need for multi-location validation as future work. revision: partial

  3. Referee: [§4] §4 (Results): While concrete MAE, percentage improvements, and ablation deltas are reported, the manuscript does not include error bars, statistical significance tests across multiple random seeds, or details on the exact train/validation/test split ratios and temporal blocking for the 6-month 15-min intervals. This weakens confidence that the 5.7% and 27.0% gains are robust rather than sensitive to a particular held-out interval.

    Authors: We acknowledge the reporting gap. The revised results section will report mean and standard deviation over five random seeds with error bars, include paired statistical significance tests (Wilcoxon signed-rank) for all reported improvements, and specify the exact split: months 1–4 for training, month 5 for validation, and month 6 for testing, using temporal blocking to avoid leakage. These additions will directly strengthen confidence in the robustness of the gains. revision: yes

standing simulated objections not resolved
  • We do not have access to additional LiDAR datasets from other corridors or cities, so cross-location or cross-city experiments cannot be performed in the current revision.

Circularity Check

0 steps flagged

No significant circularity; empirical motivation and held-out evaluation remain independent

full rationale

The paper motivates its hierarchical architecture using observed statistics (corridor flows at 65.1% volume and explaining 35.5% variance) computed on the Nashville LiDAR dataset, then trains the model and reports MAE gains plus ablations on held-out intervals from the same corpus. This is standard data-driven architecture selection followed by independent empirical testing against baselines; no equations, fitted parameters, or self-citations reduce the reported performance numbers to the motivating statistics by construction. Generalization limits are a separate concern, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that flow conservation holds at intersections and on empirical observations of corridor dominance derived from the study data; no additional free parameters or invented entities are introduced beyond standard neural-network training.

axioms (1)
  • domain assumption Flow conservation must hold: predicted inflows and outflows at each intersection and movement type must balance.
    Enforced explicitly via the physics-informed loss function described in the abstract.

pith-pipeline@v0.9.0 · 5534 in / 1336 out tokens · 53579 ms · 2026-05-10T17:11:32.064787+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

  1. [1]

    Real-time intersection turning movement flow forecasting using neural net- works,

    C. Zhanget al., “Real-time intersection turning movement flow forecasting using neural net- works,”Transportation Research Record, 2024

    work page 2024

  2. [2]

    Real-time short-term intersection turning movement flow forecasting,

    C. Watson, “Real-time short-term intersection turning movement flow forecasting,” Master’s thesis, University of Waterloo, 2024

    work page 2024

  3. [3]

    Deep learning methods for intersection traffic prediction: A survey,

    Y. Liet al., “Deep learning methods for intersection traffic prediction: A survey,”Transporta- tion Research Part C, 2024

    work page 2024

  4. [4]

    Deep learning algorithms for traffic forecasting: A comprehensive review,

    S. Afandizadeh, “Deep learning algorithms for traffic forecasting: A comprehensive review,” Journal of Advanced Transportation, 2024

    work page 2024

  5. [5]

    A survey on modern deep neural network for traffic prediction: Trends, methods and challenges,

    D. A. Tedjopurnomo, Z. Bao, B. Zheng, F. M. Choudhury, and A. K. Qin, “A survey on modern deep neural network for traffic prediction: Trends, methods and challenges,” in2023 IEEE 39th International Conference on Data Engineering (ICDE). IEEE, 2023, pp. 3795–3796

    work page 2023

  6. [6]

    Traffic flow prediction in urban built-up areas using deep learning,

    C. Li and M. G. Md Johar, “Traffic flow prediction in urban built-up areas using deep learning,” inProceedings of the 2nd International Conference on Artificial Intelligence of Things and Computing, 2025, pp. 299–304

    work page 2025

  7. [7]

    A comprehensive survey of deep learning-based traffic flow prediction models,

    R. Aliet al., “A comprehensive survey of deep learning-based traffic flow prediction models,” ICCK Transactions on Advanced Computing and Systems, 2025

    work page 2025

  8. [8]

    Traffic flow prediction using deep learning techniques in urban road networks,

    Y. Han, “Traffic flow prediction using deep learning techniques in urban road networks,” Applied Mathematics and Nonlinear Sciences, vol. 10, no. 1, 2025. [Online]. Available: https://doi.org/10.2478/amns-2025-0832

    work page doi:10.2478/amns-2025-0832 2025

  9. [9]

    Long-term traffic prediction using deep learning long short-term memory,

    A.-L. Toba, S. Kulkarni, W. Khallouli, and T. Pennington, “Long-term traffic prediction using deep learning long short-term memory,”Smart Cities, vol. 8, no. 4, p. 126, 2025

    work page 2025

  10. [10]

    A combined short-term traffic flow prediction model using vmd and deep learning,

    C. Renet al., “A combined short-term traffic flow prediction model using vmd and deep learning,”Scientific Reports, 2025

    work page 2025

  11. [11]

    Enhancement of traffic forecasting through graph neural networks,

    S. F. Ahmedet al., “Enhancement of traffic forecasting through graph neural networks,” Information Fusion, 2024. 10

    work page 2024

  12. [12]

    Urban intersection traffic flow prediction using physics-guided spatio- temporal graph neural networks,

    Y. A. Panet al., “Urban intersection traffic flow prediction using physics-guided spatio- temporal graph neural networks,”Transportation Research Part C, 2025

    work page 2025

  13. [13]

    arXiv preprint arXiv:2001.02908 (2020)

    M. Xu, W. Dai, C. Liu, X. Gao, W. Lin, G.-J. Qi, and H. Xiong, “Spatial-temporal transformer networks for traffic flow forecasting,”arXiv preprint arXiv:2001.02908, 2020

    work page arXiv 2001

  14. [14]

    Hybrid spatial–temporal graph neural network for traffic forecasting,

    P. Wang, L. Feng, Y. Zhu, and H. Wu, “Hybrid spatial–temporal graph neural network for traffic forecasting,”Information Fusion, vol. 118, p. 102978, 2025

    work page 2025

  15. [15]

    Spatial–temporal graph transformer network for traffic network flow prediction using parallel training based on cloud computing,

    Y. Zhang, S. Peng, and Y. Zhou, “Spatial–temporal graph transformer network for traffic network flow prediction using parallel training based on cloud computing,”Applied Soft Com- puting, p. 113422, 2025

    work page 2025

  16. [16]

    Spatio-temporal pivotal graph neural networks for traffic flow forecasting,

    W. Kong, Z. Guo, and Y. Liu, “Spatio-temporal pivotal graph neural networks for traffic flow forecasting,” inProceedings of the AAAI conference on artificial intelligence, vol. 38, no. 8, 2024, pp. 8627–8635

    work page 2024

  17. [17]

    Physics-informed neural networks (pinns)-based traffic state estimation: An application to traffic network,

    M. Usama, R. Ma, J. Hart, and M. Wojcik, “Physics-informed neural networks (pinns)-based traffic state estimation: An application to traffic network,”Algorithms, vol. 15, no. 12, p. 447, 2022

    work page 2022

  18. [18]

    Hierarchical predictive control of network traffic signals using link transmission model with queue dynamics,

    L. Wei, K. Ampountolas, A. Hirrle, and M. Wang, “Hierarchical predictive control of network traffic signals using link transmission model with queue dynamics,”IEEE Transactions on Intelligent Transportation Systems, 2025

    work page 2025

  19. [19]

    Traffic flow prediction based on federated learning and spatio-temporal graph neural networks,

    J. Fenget al., “Traffic flow prediction based on federated learning and spatio-temporal graph neural networks,”ISPRS International Journal of Geo-Information, 2024

    work page 2024

  20. [20]

    A parallel adaptive feature fusion framework for intersection-level traffic turning movement flow prediction,

    Y. Gong, C. Zhang, H. Wei, W. Zheng, and G. Pan, “A parallel adaptive feature fusion framework for intersection-level traffic turning movement flow prediction,” inProceedings of the 2024 2nd International Conference on Frontiers of Intelligent Manufacturing and Automation, 2024, pp. 295–300

    work page 2024

  21. [21]

    Pnns4: A parallel quadruple neural network model for intersection turning traffic flow prediction,

    C. Liuet al., “Pnns4: A parallel quadruple neural network model for intersection turning traffic flow prediction,”Canadian Journal of Civil Engineering, 2025. 11

    work page 2025