Pith. sign in

REVIEW 3 major objections 8 minor 36 references

Reviewed by Pith at T0; open to challenge.

T0 means a machine referee read the full paper against a public rubric. The mark states how deep the mechanical check went, never who wrote it. the ladder, T0–T4 →

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

T0 review · glm-5.2

Explicit geographic features cut OD flow prediction error by 24%

2026-07-07 21:07 UTC pith:QPTG6PDG

load-bearing objection Solid engineering contribution to OD flow modeling; prediction-side ablation claims are weaker than they look due to table-to-table variance and missing error bars. the 3 major comments →

arxiv 2607.05257 v1 pith:QPTG6PDG submitted 2026-07-06 cs.LG

GeoFlow: Geo-Aware Modeling of Inter-Area Relationships in Origin-Destination Flow Prediction and Generation

Zherui Huang , Guanjie Zheng , Hao Xue , Linghe Kong This is my paper
classification cs.LG
keywords origin-destination flowgeospatial feature augmentationgraph attention networkaxial attentionflow matchingmobility predictiongenerative modelingurban computing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

GeoFlow argues that origin-destination flow models fail because they encode geography as pairwise distance matrices, losing properties like relative bearing, network topology, and actual road-network travel distance that are expensive to recover from matrix form but cheap to supply directly. The paper's central claim is that explicitly augmenting area-pair representations with three additional geospatial descriptors — relative position (coordinate differences under a region-centered, PCA-aligned frame), k-hop distance (shortest path length in the road graph), and geodesic distance (weighted shortest-path travel length) — together with a split encoder that processes geometric and intrinsic attributes separately before fusing them, and an axial-global attention decoder that models competition among OD pairs sharing an origin or destination, produces state-of-the-art results on both flow prediction and flow generation across commuting, freight, and air-travel datasets. The paper demonstrates that these geospatial attributes are hard to infer implicitly from adjacency and straight-line distance matrices (a trained MLP recovers relative angles with 51% average error), which is the empirical justification for providing them as explicit input features rather than expecting deeper networks to learn them. For generation, GeoFlow pairs its encoder-decoder with continuous-time flow matching, which the paper shows trains more stably than diffusion models for the same task. The ablation studies indicate that each augmented feature and each architectural component contributes measurably, with the full feature set improving generation CPC from 0.462 to 0.527 on the commuting dataset and the full encoder-decoder improving prediction CPC from 0.567 to 0.597.

Core claim

The paper's central discovery is that geospatial attributes which graph-based OD flow models treat as implicit — relative position, k-hop topological distance, and geodesic road-network distance — are not recoverable from standard adjacency and straight-line distance matrices with useful accuracy, and that explicitly providing them as input features, combined with a geometry-intrinsic fusion encoder and an axial-global attention decoder that captures origin- and destination-conditioned competition, yields consistent improvements across three distinct mobility regimes and two task formulations. The mechanism is a three-part design: (1) geospatial feature augmentation supplies orientation, top

What carries the argument

The key machinery is the geometric-intrinsic fusion encoder, which splits area-pair attributes into geometric (relative position, straight-line, k-hop, geodesic distances encoded by MLPs) and intrinsic (POIs, demographics encoded by geography-conditioned graph attention), fuses them via concatenation and MLP; and the axial-global attention decoder, which alternates origin-wise and destination-wise self-attention (O(n^3) instead of O(n^4) for full pairwise attention) and supplements it with a compact global-attention path that pools OD pairs to area-level representations, applies self-attention at that reduced resolution (O(n^2)), then broadcasts back to the OD grid via Hadamard product. For

Load-bearing premise

The ablation studies attribute performance gains to each geospatial feature and architectural component, but this causal attribution holds only if all ablated variants received the same hyperparameter tuning effort and training budget as the full GeoFlow model; the paper does not report whether equivalent hyperparameter search was applied to each ablation, so some portion of the gains could reflect tuning differences rather than the components themselves.

What would settle it

A controlled experiment where each ablated variant receives the same hyperparameter search budget as the full model, and where the geospatial features are added to a simple baseline architecture (e.g., MLP or shallow GCN) without the proposed encoder or decoder; if the simple augmented baseline matches or approaches GeoFlow's performance, the architectural contributions would be diminished, and if the ablation gaps shrink under equal tuning, the feature-specific gains would be less certain.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the gains are attributable to the geospatial features rather than architecture, then existing graph-based OD flow models could be improved substantially by a preprocessing step that computes and supplies relative position, k-hop, and geodesic distance, without changing their core architectures.
  • The finding that flow matching trains more stably than diffusion for OD matrix generation suggests that flow matching may be a generally better fit for structured matrix-valued generative tasks where the output dimension grows quadratically with the number of entities.
  • The axial-global attention decomposition could transfer to other domains with origin-destination or bipartite-pair structure (e.g., trade flow matrices, migration tables, recommendation matrices) where full pairwise attention over all pairs is computationally prohibitive.
  • The scale-dependent performance breakdown (best on small regions, worst on large; best on high-volume OD pairs, worst on sparse long-range pairs) provides concrete targets for future work: large-region and sparse-flow regimes remain the open frontier.

Where Pith is reading between the lines

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

  • The paper does not test whether the geospatial features would help simpler architectures (e.g., a plain MLP or shallow GNN) equally well; if they do, the architectural contributions of the encoder and decoder would be less essential than the feature engineering, which would change the practical recommendation toward lightweight models with augmented inputs.
  • The coordinate normalization scheme (region-centered, PCA-aligned, scaled to [-1,1]) implicitly assumes a single contiguous region per sample; for models that need to represent flows across disconnected or non-contiguous regions, this normalization may need modification, a limitation the paper does not address.
  • The flow-matching-vs-diffusion comparison is shown only qualitatively through training curves; a controlled study varying generative backbone while holding all else fixed, with matched compute budgets and multiple seeds, would strengthen the claim that flow matching is inherently more stable for this task.
  • The cross-morphology transfer results suggest that the model learns transferable relative spatial relations, but the poor transfer to metropolitan regions from non-metropolitan training data implies that the augmented features do not fully decouple the model from city-specific structural patterns, particularly for dense, heterogeneous urban forms.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 8 minor

Summary. The paper introduces GeoFlow, a framework for origin-destination (OD) flow prediction and generation that augments area representations with geospatial attributes (relative position, k-hop distance, geodesic distance), employs a geometric-intrinsic fusion encoder combining graph attention with coordinate-aware encoders, and uses an axial-global attention decoder. For generation, the framework pairs with flow matching models. Experiments are conducted on three datasets (commuting, freight, air travel) against multiple baselines. The mathematical formulation is clean and internally consistent, the architecture is well-specified, and the flow matching formulation follows Lipman et al. (2022) correctly. The paper also provides ablation studies, generalizability analyses, and qualitative case studies.

Significance. The paper addresses a practical limitation in OD flow modeling: the neglect of explicit geospatial attributes in graph-based representations. The proposed geospatial feature augmentation is simple and well-motivated, and the analysis experiments (§4.4, Figure 2) provide empirical evidence that higher-order geographic cues are hard to recover from adjacency/distance matrices alone. The axial-global attention decoder reduces computational complexity from O(n^4) to O(n^3) for the axial path while adding an O(n^2) global pathway, which is a reasonable design. The application of flow matching to OD generation appears novel for this task domain. Code is publicly available. The generalizability experiments (Appendix C.2–C.3) are a strength, covering scale transfer, longitudinal partitions, and cross-morphology evaluation. The main comparative results (Table 1) show substantial margins over baselines, particularly on prediction tasks.

major comments (3)
  1. §4.3, Table 2 vs. Table 1: The full GeoFlow model reports CPC 0.604 on Commuting prediction in Table 1 (averaged over 3 splits) but CPC 0.597 in Table 2's ablation. This 0.007 gap exceeds several claimed ablation gains on the prediction side (e.g., feature augmentation ID 1→ID 5: 0.594→0.597, a 0.003 gain). The paper states that ablation studies 'confirm the contribution of each component' (§4.3), but without error bars or variance estimates across the 3 runs, it is unclear whether these sub-0.01 prediction-side improvements are statistically meaningful. The generation-side ablation gains are larger (CPC 0.462→0.527) and more likely robust. The authors should either report standard deviations across runs or temper the causal claims for prediction-side ablation gains that fall within the table-to-table discrepancy.
  2. §4.3, Table 2, IDs 2–4 (prediction): The feature augmentation ablation shows non-monotonic behavior on CPC for prediction. ID 1 (SL only) achieves CPC 0.594, while IDs 2–4 (adding subsets of Rel/k-hop/FF) achieve 0.591, 0.581, and 0.588 respectively—all worse than the SL-only baseline. Only the full feature set (ID 5, 0.597) marginally exceeds ID 1. The paper does not discuss this non-monotonicity. This pattern is consistent with noise rather than a clear incremental contribution of each feature. The authors should address whether this is expected and whether the prediction-side feature ablation provides reliable evidence for the contribution of individual geospatial attributes.
  3. Appendix B.4: The paper states that hyperparameters were chosen for best trade-off and that dropout was disabled throughout. However, it is not reported whether ablated variants in Table 2 received the same hyperparameter search as the full model. If the full GeoFlow model received more tuning than ablated variants, the ablation gains could be partially attributable to hyperparameter selection rather than the architectural components. The authors should clarify whether all ablation variants used identical hyperparameters or whether each was independently tuned, and ideally confirm that the same training budget was applied.
minor comments (8)
  1. §3.2.1: The coordinate normalization procedure (PCA alignment, rescaling to [-1,1]) is described in the main text and detailed in Appendix A.2, but the connection between the two descriptions could be made more explicit (e.g., a forward reference).
  2. Table 1: The 'Div.' column only applies to generation methods, but it is placed in a shared column header. A separate sub-table or clearer visual separation for generation-only metrics would improve readability.
  3. Eq. (5): The softmax is applied to Gw_geo, where G is n×n×d_g and w_geo is d_g-dimensional. The resulting S is n×n. Clarifying that softmax is applied along the last axis of G (i.e., over geographic feature dimensions for each pair) would help readers.
  4. Eq. (6): The notation (SX) is used where S is n×n and X is n×d_x. The resulting SX is n×d_x, which is then projected by W_qx. This is dimensionally consistent but the intermediate step could be stated more explicitly.
  5. §4.2: The paper notes that on Air Travel generation, GeoFlow 'remains competitive in CPC (0.457 vs. 0.486)' but this is actually a decrease relative to WEDAN. The framing as 'competitive' is reasonable but the paper should acknowledge this is the one metric where GeoFlow does not improve over the best baseline.
  6. Appendix C.6, Figure 3: The legend label 'Diffsion' should be 'Diffusion.'
  7. Table 14: The units for training/inference time (seconds) are reported but it is unclear whether these are per-sample, per-batch, or per-step times. Clarifying this would aid reproducibility.
  8. The paper claims to be 'the first work to apply flow matching in the OD flow generation task' (§1). While this may be true for OD flow specifically, the claim would be strengthened by briefly noting what generative frameworks have been used in OD generation (diffusion, GAN, etc.) and why flow matching is particularly suited.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The referee raises three points concerning statistical robustness of ablation results, non-monotonic behavior in feature ablation, and hyperparameter fairness across ablated variants. We address each below and commit to revisions where appropriate.

read point-by-point responses

  1. Referee: §4.3, Table 2 vs. Table 1: CPC discrepancy (0.604 vs. 0.597) between main results and ablation, and absence of error bars/variance estimates for sub-0.01 prediction-side ablation gains.

    Authors: The referee is correct that the 0.007 CPC discrepancy between Table 1 (0.604) and Table 2 (0.597) for the full GeoFlow model on Commuting prediction is not explained in the manuscript and that it exceeds several prediction-side ablation gains. The discrepancy arises because Table 1 reports results averaged over three independent data splits (different train/test partitions of the region set), while Table 2 reports results on a single fixed split to enable controlled component-wise comparison. We acknowledge that this difference in protocol is not stated in the paper and should be clarified. We also agree that without variance estimates, the sub-0.01 prediction-side ablation gains (e.g., ID 1→ID 5: 0.594→0.597) cannot be confidently distinguished from noise. We will address this in two ways: (1) we will add standard deviations across the three splits for all ablation variants in Table 2, and (2) we will temper the causal language for prediction-side feature ablation gains, noting that individual feature contributions on the prediction task are small relative to run-to-run variability, while the generation-side gains (CPC 0.462→0.527) are substantially larger and more robust. The core claim that the full feature set benefits generation is well-supported; the claim for prediction will be stated more cautiously. revision: yes

  2. Referee: §4.3, Table 2, IDs 2–4 (prediction): Non-monotonic CPC behavior where partial feature subsets (IDs 2–4) perform worse than SL-only (ID 1, CPC 0.594), and only the full set (ID 5, 0.597) marginally exceeds it.

    Authors: The referee correctly identifies a pattern in the prediction-side ablation that we did not discuss. The non-monotonic behavior—where adding subsets of features (Rel, k-hop, FF) individually or in pairs yields CPC values of 0.591, 0.581, and 0.588, all below the SL-only baseline of 0.594—is consistent with noise on the prediction task, as the referee notes. We agree that this pattern does not provide reliable evidence for the incremental contribution of each individual geospatial attribute in the prediction setting. In contrast, the generation-side ablation shows monotonic improvement (0.462→0.515→0.514→0.510→0.527 in CPC, with consistent NRMSE and JSD reductions), which does support the value of the full feature set. We will add a discussion of this non-monotonicity in the revised manuscript, explicitly acknowledging that prediction-side feature ablation does not cleanly isolate individual feature contributions, and that the evidence for feature augmentation is primarily carried by the generation results and the analysis experiments in §4.4 (which show that higher-order geographic attributes are difficult to recover from adjacency/distance matrices alone). We will also note that the features are designed to be complementary rather than independently additive, which is consistent with the full set outperforming any partial subset. revision: yes

  3. Referee: Appendix B.4: Whether ablated variants in Table 2 received the same hyperparameter search as the full model, or whether the full model was more tuned.

    Authors: We appreciate this concern about hyperparameter fairness. To clarify: all ablation variants in Table 2 used the same hyperparameters as the full GeoFlow model—they were not independently tuned. The hyperparameter configuration described in Appendix B.4 (hidden dimension 32, two encoder layers, two decoder layers, four attention heads, dropout disabled, learning rate 1e-3, batch size 64) was selected via sensitivity analysis on the full model and then held fixed across all ablated variants. No variant-specific hyperparameter search was performed. This means the ablation gains (or lack thereof) reflect architectural/feature differences rather than differential tuning. We will add an explicit statement to Appendix B.4 confirming that all ablation variants share identical hyperparameters and training budgets, to prevent any ambiguity on this point. revision: yes

Circularity Check

0 steps flagged

No significant circularity found; the paper is self-contained with one non-load-bearing self-citation.

full rationale

The paper's derivation chain is self-contained and does not exhibit circular reasoning. (1) The geospatial features (relative position, k-hop distance, geodesic distance) are computed from standard geographic data (coordinates, road network adjacency, shortest paths) via preprocessing (Appendix A.2), not fitted to target OD flows. (2) The flow matching formulation (Appendix A.1, Eqs. 26-30) is derived entirely from Lipman et al. (2022), an external reference, with standard linear-Gaussian interpolation paths and Euler sampling. (3) The encoder (Eqs. 3-8) uses graph attention from Veličković et al. (2017) and standard MLPs; the decoder (Eqs. 9-21) uses axial attention from Ho et al. (2019) and self-attention from Vaswani et al. (2017) — all external. (4) The one self-citation, Huang et al. (2025), appears alongside Lipman et al. (2022) as a supporting reference for the claim that flow matching provides 'higher stability, efficiency, and generalization than diffusion models.' This citation is not load-bearing: the actual flow matching formulation in Appendix A.1 is fully derived from Lipman et al. (2022), and the empirical comparison between flow matching and diffusion (Appendix C.6, Fig. 3) is an independent experiment within this paper. (5) The ablation studies (Table 2) compare architecturally distinct model variants; no ablation 'prediction' reduces to a fitted parameter by construction. (6) The analysis experiments (Table 3, Fig. 2) are independent measurements (matrix similarity norms, MLP reconstruction errors) that support the motivation for explicit feature augmentation without circular dependency. The reader's concern about the 0.007 CPC discrepancy between Tables 1 and 2 is a statistical power concern, not a circularity concern. Score 1 reflects the minor non-load-bearing self-citation.

Axiom & Free-Parameter Ledger

9 free parameters · 5 axioms · 0 invented entities

GeoFlow introduces no new physical entities, particles, forces, or postulated objects. All components (graph attention, axial attention, flow matching, MLPs) are standard neural network building blocks. The geospatial features (relative position, k-hop distance, geodesic distance) are computed from existing geographic data, not invented. The free parameters are standard learnable neural network weights and a few hyperparameters. The axioms are domain assumptions about mobility patterns and representation properties, most of which receive at least partial empirical support within the paper.

free parameters (9)
  • w_geo
    Learnable weighted vector in R^{d_g} for computing the score matrix S (Eq. 5), used to modulate query formation in the encoder. Trained end-to-end.
  • W_qx, W_kx
    Learnable projection matrices in R^{d_x x d_h} for the graph attention computation (Eq. 6). Trained end-to-end.
  • phi_g, phi_x, phi_f, phi_h, phi_out, phi_p, phi_gen, psi
    MLP parameters for geometric encoding, intrinsic encoding, fusion, projection, output prediction, and generation velocity prediction. All trained end-to-end.
  • W_q, W_k, W_v (decoder)
    Learnable matrices for axial and global self-attention in the decoder (Eq. 9). Trained end-to-end.
  • alpha, beta (generation loss)
    Hyperparameters balancing reconstruction, distributional discrepancy, and diversity in the generation loss (Eq. 2). Specific values not reported in the main text.
  • tau (affinity kernel) = median of positive finite distances
    Bandwidth for exponential kernel in affinity construction (Eq. 31, Appendix A.2). Set to median distance, not fitted to target.
  • d_e, d_h, d_z = 32 (d_e), not specified (d_h, d_z)
    Embedding and hidden dimensions. d_e=32 reported in Appendix B.4; d_h and d_z not explicitly stated.
  • L_a, L_g = 2, 2
    Number of axial-attention layers and global-attention layers. Reported as 2 each in Appendix B.4.
  • n_steps (flow matching integration)
    Number of Euler integration steps for flow matching sampling (Eq. 30). Not explicitly reported.
axioms (5)
  • domain assumption OD pairs sharing the same origin or destination exhibit stronger correlations than unrelated pairs.
    Section 3.2.3: 'Empirically, OD pairs that share an origin or share a destination are more strongly coupled.' This motivates the axial attention design. It is a plausible domain assumption but is stated without quantitative evidence in the main text.
  • domain assumption Higher-order geospatial attributes (relative angles, k-hop, geodesic distances) cannot be effectively recovered from adjacency and straight-line distance matrices by neural networks.
    Section 4.4 and Figure 2: An MLP trained to predict these attributes from matrices shows large reconstruction errors (51.1% relative error for angles). This supports the design choice to provide features explicitly. The experiment is small-scale but provides direct evidence.
  • domain assumption Geometric attributes (coordinates, distances) and intrinsic attributes (POIs, demographics) have fundamentally different semantics, scales, and propagation behaviors, justifying separate encoding.
    Section 3.2: 'These two categories differ in semantics, scale, and propagation behavior.' This is a reasonable modeling assumption but is not formally proven.
  • domain assumption Flow matching provides higher stability, efficiency, and generalization than diffusion models for OD flow generation.
    Section 1 and Appendix C.6. Supported by the training dynamics comparison in Figure 3, which shows diffusion model instability. The comparison is on a single dataset configuration.
  • domain assumption PCA-aligned, normalized relative coordinates provide a reference-frame-invariant representation suitable for transfer across regions.
    Section 3.2.1 and Appendix A.2. The coordinate normalization (center, PCA align, scale to [-1,1]) is assumed to remove reference-origin sensitivity. Appendix C.3 provides cross-morphology transfer results that partially support this.

pith-pipeline@v1.1.0-glm · 27314 in / 3773 out tokens · 344284 ms · 2026-07-07T21:07:32.446851+00:00 · methodology

0 comments
read the original abstract

Origin-destination (OD) flow modeling underpins urban planning and mobility analysis, but prevailing graph-based methods often neglect salient geographic attributes, limiting their ability to model long-range and multi-area dependencies. In this paper, we introduce GeoFlow, a novel framework that (i) augments area representations with geospatial attributes, including relative positions, k-hop and geodesic distances, (ii) employs a specialized geometric-intrinsic fusion encoder design that combines graph attention for intrinsic area signals with coordinate-aware encoders for global structure, and (iii) adopts an axial-global attention decoder to capture OD-specific competitive dependencies. For OD flow generation, GeoFlow is paired with flow matching models to produce more authentic and diverse mobility samples. Empirically, GeoFlow achieves superior performance in predictive accuracy, while substantially improving generative fidelity and diversity. Ablation and analytical studies confirm the contribution of each component. Code is available at https://github.com/ZheruiHuang/GeoFlow.

Figures

Figures reproduced from arXiv: 2607.05257 by Guanjie Zheng, Hao Xue, Linghe Kong, Zherui Huang.

Figure 1
Figure 1. Figure 1: Framework of GeoFlow. The framework comprises three main components: the augmented geospatial relation descriptors, the encoder for fusing geometric and intrinsic attributes, and the axial–global attention–based decoder. ogous notation similarly applies to tensors of order three and higher. 3.2.1. GEOSPATIAL FEATURE AUGMENTATION Since graph-based approaches typically store geographical relationships as adj… view at source ↗
Figure 2
Figure 2. Figure 2: Prediction errors when inferring higher-order geospatial attributes from adjacency and straight-line distance matrices. mance, as shown in Tab. 2. The full encoder-decoder archi￾tecture achieves the best results (ID 9). For prediction, it improves CPC/NRMSE/JSD from 0.567/2.134/0.201 to 0.597/1.730/0.171 over ID 6; for generation, it im￾proves the corresponding metrics from 0.510/6.780/0.209 to 0.527/4.330… view at source ↗
Figure 3
Figure 3. Figure 3: Training dynamics comparison between flow-matching and diffusion models. Flow-matching demonstrates steady improvements across metrics, while diffusion exhibits instability and performance degradation [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative case study of learned attention in Barbour County, Alabama, United States. Panels from left to right show the geographic layout of areas, the global attention heatmap, axial attention over destinations for origin area 6, and axial attention over destinations for origin area 0. By contrast, training on medium and large areas is most effective when the evaluation target is medium or large (IDs 10… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative comparison of OD flows. For each selected region, we show the geographic map, the ground truth, the model prediction, and three independently generated samples. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 9 internal anchors

  1. [1]

    Zipf, George Kingsley , journal=. The. 1946 , publisher=

    work page 1946

  2. [2]

    Nature , volume=

    A universal model for mobility and migration patterns , author=. Nature , volume=. 2012 , publisher=

    work page 2012

  3. [3]

    Proceedings of the 1st ACM SIGCAS Conference on Computing and Sustainable Societies , pages=

    A machine learning approach to modeling human migration , author=. Proceedings of the 1st ACM SIGCAS Conference on Computing and Sustainable Societies , pages=

    work page

  4. [4]

    Proceedings of the 2nd acm sigspatial international workshop on ai for geographic knowledge discovery , pages=

    Enhancing trip distribution prediction with twitter data: comparison of neural network and gravity models , author=. Proceedings of the 2nd acm sigspatial international workshop on ai for geographic knowledge discovery , pages=

    work page

  5. [5]

    Computers, Environment and Urban Systems , volume=

    Trip distribution modeling with Twitter data , author=. Computers, Environment and Urban Systems , volume=. 2019 , publisher=

    work page 2019

  6. [6]

    Nature communications , volume=

    A deep gravity model for mobility flows generation , author=. Nature communications , volume=. 2021 , publisher=

    work page 2021

  7. [7]

    Proceedings of the AAAI conference on artificial intelligence , volume=

    Learning geo-contextual embeddings for commuting flow prediction , author=. Proceedings of the AAAI conference on artificial intelligence , volume=

    work page

  8. [8]

    Transportation , volume=

    A complex network perspective for characterizing urban travel demand patterns: graph theoretical analysis of large-scale origin--destination demand networks , author=. Transportation , volume=. 2017 , publisher=

    work page 2017

  9. [9]

    Complexity-aware Large Scale Origin-Destination Network Generation via Diffusion Model

    Complexity-aware large scale origin-destination network generation via diffusion model , author=. arXiv preprint arXiv:2306.04873 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  10. [10]

    ACM Computing Surveys , volume=

    An interdisciplinary survey on origin-destination flows modeling: Theory and techniques , author=. ACM Computing Surveys , volume=. 2024 , publisher=

    work page 2024

  11. [11]

    The Thirteenth International Conference on Learning Representations , year=

    A Large-scale Dataset and Benchmark for Commuting Origin-Destination Flow Generation , author=. The Thirteenth International Conference on Learning Representations , year=

    work page

  12. [12]

    Journal of urban planning and development , volume=

    Origin--destination matrix estimation and prediction from socioeconomic variables using automatic feature selection procedure-based machine learning model , author=. Journal of urban planning and development , volume=. 2021 , publisher=

    work page 2021

  13. [13]

    Highway Research Board Bulletin , year=

    A new method of trip distribution in an urban area , author=. Highway Research Board Bulletin , year=

    work page

  14. [14]

    International conference on machine learning , pages=

    Netgan: Generating graphs via random walks , author=. International conference on machine learning , pages=. 2018 , organization=

    work page 2018

  15. [15]

    TransFlower: An Explainable Transformer-Based Model with Flow-to-Flow Attention for Commuting Flow Prediction

    TransFlower: An explainable transformer-based model with flow-to-flow attention for commuting flow prediction , author=. arXiv preprint arXiv:2402.15398 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    2007 , publisher=

    Cities and complexity: understanding cities with cellular automata, agent-based models, and fractals , author=. 2007 , publisher=

    work page 2007

  17. [17]

    2024 11th International Conference on Soft Computing & Machine Intelligence (ISCMI) , pages=

    A survey on origin-destination flow prediction , author=. 2024 11th International Conference on Soft Computing & Machine Intelligence (ISCMI) , pages=. 2024 , organization=

    work page 2024

  18. [18]

    Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining , pages=

    Practical synthetic human trajectories generation based on variational point processes , author=. Proceedings of the 29th ACM SIGKDD conference on knowledge discovery and data mining , pages=

    work page

  19. [19]

    ACM Computing Surveys (CSUR) , volume=

    A survey on deep learning for human mobility , author=. ACM Computing Surveys (CSUR) , volume=. 2021 , publisher=

    work page 2021

  20. [20]

    Transportation Research Part C: Emerging Technologies , volume=

    Short-term origin-destination demand prediction in urban rail transit systems: A channel-wise attentive split-convolutional neural network method , author=. Transportation Research Part C: Emerging Technologies , volume=. 2021 , publisher=

    work page 2021

  21. [21]

    Machine learning , volume=

    Random forests , author=. Machine learning , volume=. 2001 , publisher=

    work page 2001

  22. [22]

    Advances in neural information processing systems , volume=

    Support vector regression machines , author=. Advances in neural information processing systems , volume=

    work page

  23. [23]

    Computer Science Review , volume=

    A survey on deep learning and its applications , author=. Computer Science Review , volume=. 2021 , publisher=

    work page 2021

  24. [24]

    Flow Matching for Generative Modeling

    Flow matching for generative modeling , author=. arXiv preprint arXiv:2210.02747 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    Forty-second International Conference on Machine Learning , year=

    Flow Matching for Denoised Social Recommendation , author=. Forty-second International Conference on Machine Learning , year=

    work page

  26. [26]

    Wiley interdisciplinary reviews: computational statistics , volume=

    Principal component analysis , author=. Wiley interdisciplinary reviews: computational statistics , volume=. 2010 , publisher=

    work page 2010

  27. [27]

    Flow Matching Guide and Code

    Flow matching guide and code , author=. arXiv preprint arXiv:2412.06264 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  28. [28]

    Advances in Neural Information Processing Systems , volume=

    Matrix factorisation and the interpretation of geodesic distance , author=. Advances in Neural Information Processing Systems , volume=

    work page

  29. [29]

    International conference on machine learning , pages=

    E(n) equivariant graph neural networks , author=. International conference on machine learning , pages=. 2021 , organization=

    work page 2021

  30. [30]

    On the Bottleneck of Graph Neural Networks and its Practical Implications

    On the bottleneck of graph neural networks and its practical implications , author=. arXiv preprint arXiv:2006.05205 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  31. [31]

    International conference on artificial intelligence and statistics , pages=

    Positional encoder graph neural networks for geographic data , author=. International conference on artificial intelligence and statistics , pages=. 2023 , organization=

    work page 2023

  32. [32]

    Axial Attention in Multidimensional Transformers

    Axial attention in multidimensional transformers , author=. arXiv preprint arXiv:1912.12180 , year=

    work page internal anchor Pith review Pith/arXiv arXiv 1912

  33. [33]

    Advances in neural information processing systems , volume=

    Attention is all you need , author=. Advances in neural information processing systems , volume=

    work page

  34. [34]

    Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

    Geometric deep learning: Grids, groups, graphs, geodesics, and gauges , author=. arXiv preprint arXiv:2104.13478 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  35. [35]

    On Measuring Long-Range Interactions in Graph Neural Networks

    On Measuring Long-Range Interactions in Graph Neural Networks , author=. arXiv preprint arXiv:2506.05971 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    Graph Attention Networks

    Graph attention networks , author=. arXiv preprint arXiv:1710.10903 , year=

    work page internal anchor Pith review Pith/arXiv arXiv