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Learning Local Heterogeneity and Cross-Region Context for Large-Scale Traffic Forecasting

Qi Feng, Zidong Wang, Bo Li, Xiaoguang Gao, Jiayu Zhang, Chenfeng Wang, Kaifang Wan

arXiv:2609.27637v1cs.LGcs.AI

TL;DR

Large-scale traffic forecasting must capture heterogeneous local dependencies while acquiring long-range context efficiently. LoReST combines relation-aware neighborhood aggregation with region-level interaction. On four LargeST datasets, it achieves the best results across evaluated horizons and average metrics.

  • Problem

    Large-scale forecasting must model complex spatial dependencies under resource constraints, while neighboring nodes can have heterogeneous relationships based on road identity and travel direction.

    Source: §I · pp. 1–2

  • Method

    LoReST jointly models local neighborhoods and road-network regions, using relation-specific transformations locally and pooled regional representations with inter-region attention.

    Source: §I · p. 2

  • Results

    LoReST achieves the best results across evaluated horizons and average metrics on four datasets, reducing average MAE by 6.74% on SD versus the best-performing baseline.

    Source: B. Main Results(RQ1) · p. 7

  • Takeaways & Limitations

    The framework learns node-level forecasting representations by combining local dependencies with long-range regional context.

    Source: §VI · p. 11

Abstract

from arXiv · show

Traffic flow forecasting is essential to intelligent transportation systems. Large-scale traffic forecasting requires jointly modeling local spatial dependencies and cross-region context.Spatial dependencies between geographically neighboring nodes are heterogeneous due to differences in road identity and travel direction, while acquiring global information through allpairs node interactions incurs substantial computational costs. Therefore, capturing local heterogeneity while efficiently acquiring long-range context remains an important challenge in largescale traffic forecasting. To address these challenges, we propose LoReST, a Local-Region Spatial Temporal network that models spatial dependencies at two complementary granularities: node neighborhoods and road network regions. Specifically, relation-aware local aggregation captures heterogeneous dependencies within geographic neighborhoods through road and direction specific feature transformations. Cross-region interaction constructs region representations through mean pooling, exchanges long range context via inter-region attention, and broadcasts it back to nodes. By integrating local information aggregation with crossregion interaction, LoReST is able to effectively achieve spatial dependency learning in large-scale road networks. Experiments on four datasets of the LargeST benchmark show average relative reductions of 4.78%, 3.60%, and 5.75% in MAE, RMSE, and MAPE, respectively.

I. Introduction T

Large-scale traffic forecasting must capture spatial dependencies while controlling computation as networks grow. LoReST combines relation-aware local modeling with region-level context interaction.

I. Introduction T

  • Traffic forecasting on networks with thousands of nodes must model complex spatial dependencies under limited computational resources.Distant sensors may also share traffic patterns, but fine-grained interactions among all nodes incur substantial computation and memory costs.Source: §I · pp. 1–2
  • Existing scalable approaches include identity-based lightweight models, linearized global convolution, random projections, and spatial patching to balance accuracy and efficiency.The introduction cites STID, BigST, RPMixer, and PatchSTG as examples.Source: §I · p. 1
  • Geographically adjacent nodes can differ in road identity and travel direction, producing distinct traffic association patterns despite their proximity.Geographic proximity is presented as a useful prior for selecting candidate neighbors, not as evidence of homogeneous relationships.Source: §I · pp. 1–2
  • LoReST organizes spatial interactions at node and region levels to jointly model local associations and cross-region context while balancing modeling capability and efficiency.The framework uses spatial prior knowledge to organize interactions at both granularities.Source: §I · p. 2
  • Relation-aware local aggregation applies distinct feature transformations to neighbor groups defined by road identity and travel direction.The groups are same-road same-direction, same-road opposite-direction, and different-road neighbors.Source: §I · p. 2
  • Cross-region interaction pools nodes into compact regional representations, exchanges context through inter-region attention, and broadcasts it back to nodes.This mechanism is proposed to capture long-range spatial dependencies.Source: §I · p. 2
  • LoReST outperforms all compared methods on each of the four LargeST datasets, achieving state-of-the-art forecasting performance.The introduction reports comprehensive experiments on real-world benchmark datasets.Source: §I · p. 2

A. Spatial Dependency Modeling for Traffic Forecasting

The section reviews graph-based spatial dependency modeling and efficiency strategies, then defines traffic observations and the forecasting objective.

A. Spatial Dependency Modeling for Traffic Forecasting

  • STGCN [5] and DCRNN [7] use predefined graph convolution, while GWNet [8], AGCRN, and MTGNN learn graph structure; later methods model dynamic dependencies –.The reviewed dynamic approaches include graph learning, attention, and delay-aware transformations.Source: A. Spatial Dependency Modeling for… · pp. 2–3
  • Dense spatial correlations have quadratic node-count costs, while message passing needs repeated steps for long-range information and can oversmooth representations.The review also notes Neural ODE approaches – and efficient attention approaches such as STWave.Source: A. Spatial Dependency Modeling for… · p. 3

B. Efficient Forecasting on Large-Scale Road Networks

  • Large-scale efficiency approaches reduce spatial computation through linear-complexity mechanisms or by reorganizing node interactions into spatial partitions.Examples include BigST, MAGE, RPMixer, PatchSTG, and SqLinear [33].Source: B. Efficient Forecasting on… · p. 3

A. Traffic Flow Series

  • A sensor's traffic series is a length-H sequence, and observations across N sensors form a network matrix X in R^(N×H).The sensors are also referred to as nodes.Source: A. Traffic Flow Series · p. 3

B. Traffic Flow Forecasting

  • The forecasting objective maps historical network observations X_t to predictions for the next F time steps, using sensor locations as spatial prior information.The predicted traffic flow is represented as Y-hat_t, while P contains geographic prior knowledge and theta denotes learnable parameters.Source: B. Traffic Flow Forecasting · p. 3

IV. Methodology

LoReST builds node representations from traffic history and spatial-temporal identities, then combines local aggregation with cross-region interaction before decoding future traffic predictions.

IV. Methodology

  • Preprocessing constructs candidate neighborhoods and partitions the road network into regions, supplying structural priors to the two spatial modules.The workflow also includes embedding, spatial encoding, and prediction decoding.Source: §IV · p. 3, Figure 2 · p. 4

A. Model Architecture

  • Node representations concatenate projected traffic histories with spatial, time-of-day, and day-of-week identity embeddings.The identity embeddings distinguish node-specific characteristics and recurring temporal patterns.Source: 1) Spatial Temporal Embedding · p. 4
  • Each spatial encoder layer applies relation-aware local aggregation, cross-region interaction, and a node-wise feed-forward network with residual connections.The local module first aggregates candidate-neighbor information; cross-region interaction then returns regional context to nodes.Source: 2) Spatial Encoder · p. 4
  • A shared linear decoder maps the final node representations to predictions for the next F time steps.It produces all future-step predictions simultaneously.Source: 3) Decoder · p. 5

B. Relation-aware Local Aggregation

Relation-aware local aggregation uses geographically nearby sensors as candidates but transforms their messages according to road identity and travel direction. This design reflects differing traffic associations among the relation types.

B. Relation-aware Local Aggregation

  • Same-road, same-direction neighbors have the highest observed and seasonality-adjusted correlations with target sensors among the three relation types.After removing weekly seasonality, same-road, opposite-direction neighbors correlate more highly than different-road neighbors.Source: B. Relation-aware Local Aggregation · p. 5
  • Each node’s candidate neighborhood comprises its k nearest other nodes by geographic distance, with indices fixed after preprocessing.The method uses the Haversine formula to measure great-circle distance.Source: 1) Neighbor Selection · p. 5
  • The candidates are divided into same-road/same-direction, same-road/opposite-direction, and different-road groups, whose features receive independent transformations.The three transformed group representations are summed to form the local message.Source: 2) Relation-Aware Neighbor Aggregation · p. 5
  • Neighbor representations are projected into a low-dimensional space, summed by relation, and normalized by the total candidate count k.The resulting message is projected back to the hidden dimension and added to the target representation through a residual connection.Source: 2) Relation-Aware Neighbor Aggregation · pp. 5–6

C. Cross-Region Spatial Interaction

LoReST partitions the road network into balanced, compact regions and uses attention among region representations to exchange long-range context. Regional messages are broadcast to nodes while preserving their local representations.

C. Cross-Region Spatial Interaction

  • Recursive bisection partitions nodes into nonempty regions, balancing region sizes while promoting geographic compactness and consistency of road affiliation.The partition uses sensor coordinates and road identifiers and is built during preprocessing from static metadata.Source: 1) Region Partitioning · p. 6
  • Each region representation is the mean of its constituent nodes’ locally aggregated representations, and self-attention learns dependencies across regions.The attention output contains region representations enriched with cross-region context.Source: 2) Cross-Region Attention · p. 6
  • Projected regional outputs are broadcast to their constituent nodes as shared regional messages, while residual connections retain individual local representations.The resulting node representations are denoted Hcr.Source: 2) Cross-Region Attention · p. 6

D. Model Training and Complexity Analysis

LoReST is trained by minimizing mean absolute error over valid node–time observations. Its spatial computation combines local neighbor aggregation with region-level attention, avoiding dense all-pairs node interactions.

D. Model Training and Complexity Analysis

  • LoReST minimizes mean absolute error over node–time pairs with valid ground-truth observations.The parameters are learned by gradient descent.Source: 1) Model Training · p. 6
  • Preprocessing neighbor selection typically costs O(N log N + Nk), while balanced recursive region partitioning has an upper bound of O(N log N log R).Both operations occur before training and do not participate in gradient-based optimization.Source: 2) Complexity Analysis · p. 6
  • With M spatial encoder layers, the forward-pass complexity is O(M(Nk + R^2)), linear in node count when k, R, and M are fixed.The components are O(Nk) local aggregation, O(R^2) inter-region attention, and O(N) pooling and broadcasting; R ≪ N and k ≪ N.Source: 2) Complexity Analysis · p. 6

V. Experiment

The experiment section frames evaluation around forecasting performance, component contributions, parameter sensitivity, relation-specific dependencies, and temporal behavior. It also points to statistics for the LargeST datasets.

V. Experiment

  • RQ1 asks whether LoReST outperforms existing methods across road-network scales and forecasting horizons.The section also identifies Table I as reporting LargeST dataset statistics.Source: §V · p. 6, Table I · p. 7
  • RQ2 asks how local aggregation and cross-region interaction contribute to performance and whether their benefits are complementary.RQ3 examines how key parameters affect forecasting performance.Source: §V · p. 6
  • RQ4 tests whether LoReST learns different dependencies for different road relations, while RQ5 examines peaks, rapid transitions, and temporal trends across forecasting horizons.Source: §V · p. 6

A. Experiment Settings

Experiments evaluate LoReST on four LargeST datasets against representative forecasting baselines. The reported results show strong forecasting performance alongside relatively low computational overhead.

A. Experiment Settings

  • LoReST uses 2019 data from SD, GBA, GLA, and CA, split chronologically 6:2:2, to predict 12 future steps from the preceding 12.The study evaluates MAE, RMSE, and MAPE, with lower values indicating better performance.Source: 1) Datasets · p. 7, 3) Evaluation Metrics · p. 7
  • The comparison covers graph, lightweight MLP, linear-complexity graph, and spatial-partitioning methods, using official configurations for four retrained baselines and PatchSTG-reported results for the others.Experiments use BasicTS, AdamW, four spatial encoder layers, and an NVIDIA RTX 4090 GPU.Source: 2) Baselines · p. 7, 4) Implementation Details · p. 7

B. Main Results(RQ1)

  • Prior comparisons describe STID as competitive without explicit spatial modeling and PatchSTG as combining local and global information through explicit spatial modeling.Source: B. Main Results(RQ1) · p. 7
  • The results attribute LoReST’s performance to complementary granularities: relation-aware node aggregation preserves local heterogeneity, while compact regions exchange long-range context.The design avoids all-pairs node interactions while retaining fine-grained local information.Source: B. Main Results(RQ1) · p. 7
  • LoReST leads across evaluated horizons and average metrics on all four datasets, reducing average MAE versus each metric’s best baseline by 6.74% (SD), 4.15% (GBA), 4.88% (GLA), and 3.33% (CA).The corresponding mean relative reductions across MAE, RMSE, and MAPE are 6.25%, 3.84%, 5.42%, and 3.56% on SD, GBA, GLA, and CA, respectively.Source: B. Main Results(RQ1) · p. 7, Table II · p. 8
  • On CA, LoReST has 1.790 million parameters and reduces training and inference times versus PatchSTG by approximately 49.2% and 44.4%, respectively.Against SqLinear, it uses approximately 5.3% more training time, has comparable inference time, and reduces MAE by approximately 7.1%; MAGE is fastest but has higher forecasting error.Source: B. Main Results(RQ1) · pp. 7, 9, Table III · p. 9

C. Ablation Study(RQ2)

Ablations indicate that local relation-aware aggregation and cross-region interaction both contribute to performance, with cross-region removal producing the larger MAE and RMSE increases. The component tests also favor relation-specific neighbor processing and mean-pooled region representations over the tested alternatives.

C. Ablation Study(RQ2)

  • Removing either RLA or CRSI degrades performance, and removing both causes further deterioration; CRSI removal increases MAE and RMSE more than RLA removal across all four datasets.Identity embeddings alone are insufficient to fully capture spatial dependencies.Source: C. Ablation Study(RQ2) · p. 9
  • Sharing one transformation across road-relation categories degrades performance on all four datasets, and restricting aggregation to same-road, same-direction neighbors underperforms the full model.Opposite-direction and different-road neighbors can provide complementary information; restricted or mixed local information can even underperform removing local aggregation on some datasets.Source: C. Ablation Study(RQ2) · p. 9
  • Removing intra-region mean pooling degrades all forecasting metrics across four datasets, while preserving more node-level interaction details does not necessarily help within this architecture.Source: C. Ablation Study(RQ2) · p. 9
  • Replacing RLA and CRSI with intra-region and inter-region attention reduces performance, making the tested dual-attention alternative less effective than LoReST’s combined design.Source: C. Ablation Study(RQ2) · p. 9

D. Hyperparameter Study(RQ3)

The study tests how neighbor count, region count, and spatial encoder depth affect LoReST. Its findings favor balanced local coverage and appropriate region granularity over simply increasing these settings.

Number of neighbors

Number of regions

  • Finer partitioning does not necessarily improve forecasting; an appropriate region granularity supports effective cross-region context.The study varies r over [8, 16, 32, 64, 128], fixing k=24 and M=4.Source: D. Hyperparameter Study(RQ3) · p. 9

Spatial encoder layers

  • Forecasting performance begins to degrade at M=5, suggesting effective use of spatial knowledge does not require excessive depth.The study compares M values [2, 3, 4, 5], fixing k=24 and r=16.Source: D. Hyperparameter Study(RQ3) · p. 10

E. Case Study

The case study examines learned local relation transformations, message strengths across relation types, and predictions at multiple horizons. It reports differentiated transformations and stronger same-road, same-direction messages, while LoReST tracks traffic trends in the illustrated forecasts.

Analysis of Local Heterogeneity (RQ4)

Prediction Visualization (RQ5)

  • Across the illustrated CA forecasts, LoReST aligns more closely with ground truth and maintains trend tracking as the horizon increases.The visualization compares models at 3-, 6-, and 12-step horizons; all generally capture periodic patterns, but differ during peaks and rapid transitions.Source: 2) Prediction Visualization(RQ5) · p. 11, Figure 9 · p. 11

VI. Conclusion and Future Work

LoReST jointly models node-level local dependencies and region-level long-range context for traffic forecasting. The conclusion reports state-of-the-art performance on four LargeST datasets and identifies pretrained time-series models and unseen-road-network zero-shot forecasting as future work.

Conclusion

  • LoReST combines relation-aware local aggregation with pooled regional representations and inter-region attention to enrich node representations beyond local neighborhoods.Its spatial priors include geographic locations, road identities, and travel directions.Source: §VI · p. 11
  • Ablation studies validate the effectiveness of local relation modeling and cross-region context interaction.Source: §VI · pp. 11–12

Future Work

  • Future work will incorporate spatial prior knowledge into pretrained time-series foundation models for zero-shot forecasting on unseen road networks.Source: §VI · p. 12

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