DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation

Mengzhu Wang; Nan Yin; Siyang Gao; Xinwang Liu; Yingxu Wang

arxiv: 2602.00656 · v2 · submitted 2026-01-31 · 💻 cs.LG

DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation

Yingxu Wang , Xinwang Liu , Mengzhu Wang , Siyang Gao , Nan Yin This is my paper

Pith reviewed 2026-05-16 09:02 UTC · model grok-4.3

classification 💻 cs.LG

keywords graph domain adaptationRiemannian geometryflow matchingstructure preservationpolar coordinatesmanifold learningdomain shiftgeodesic transport

0 comments

The pith

Graph domain adaptation preserves label-relevant topology by embedding representations in geodesic polar coordinates on constant-curvature manifolds and learning flow-based transport.

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

The paper establishes that Euclidean adversarial methods for graph domain adaptation entangle and suppress topology important for labels while producing unstable optimization under large shifts. It proposes to embed graph representations on a constant-curvature manifold expressed in geodesic polar coordinates so that radial distances and angular directions can be aligned separately. Polar endpoint regularization uses univariate Wasserstein alignment on radial scales and confidence-filtered alignment on angles, with radial magnitude modulating pseudo-label reliability. Topology-conditioned polar flow matching then couples compatible source and target samples through a normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis links polar discrepancies and flow error to target risk, and experiments under diverse shifts show consistent gains over prior methods.

Core claim

DisRFM embeds graph representations on a constant-curvature manifold and expresses them in geodesic polar coordinates. Polar endpoint regularization calibrates topology-sensitive radial scales via univariate Wasserstein alignment and preserves scale-normalized class semantics through confidence-filtered angular alignment, with radial magnitude modulating pseudo-label reliability. Topology-conditioned polar flow matching couples class-compatible source and target samples by a normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis characterizes the structural risk of unconditional domain confusion and relates polar and flow-

What carries the argument

Geodesic polar coordinates on constant-curvature manifolds combined with topology-conditioned polar flow matching that aligns radial scales and angular semantics separately

If this is right

Polar discrepancies and flow error bound the target risk of the adapted classifier.
Radial magnitude directly modulates the reliability of pseudo-labels during adaptation.
The method reduces structural degeneration by separating radial and angular alignment.
Unconditional domain confusion carries a quantifiable structural risk that the polar approach mitigates.

Where Pith is reading between the lines

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

The radial-angular separation may extend to other manifold-valued data such as molecular graphs or 3D point clouds.
Similar polar transport costs could stabilize adversarial training in non-graph settings with geometric structure.
Experiments on manifolds with variable curvature would test whether constant curvature is essential or merely convenient.

Load-bearing premise

That expressing graph representations in geodesic polar coordinates on a constant-curvature manifold preserves label-relevant topology without distortions that the subsequent regularization cannot correct.

What would settle it

A dataset with strong topological shifts critical to labels where removing the polar regularization causes DisRFM accuracy to fall below Euclidean baselines.

Figures

Figures reproduced from arXiv: 2602.00656 by Mengzhu Wang, Nan Yin, Siyang Gao, Xinwang Liu, Yingxu Wang.

**Figure 1.** Figure 1: (a) (c) show Structural Degeneration and Optimization Instability in Euclidean adversarial alignment. (b) (d) describe the Riemannian polar coordinates that enable disentangled structure-semantics encoding, while flow matching ensures stable convergence. mantic identity is captured by the angular component, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: Training stability comparisons. performance in 8 out of 12 scenarios. This supports our theoretical analysis in Proposition 4.1, validating that hyperbolic space’s exponential growth is vital for handling hierarchies with minimal distortion. It effectively avoids the capacity limits of Euclidean space. Furthermore, this success proves that Riemannian Flow Matching leverages metric coupling, forcing transp… view at source ↗

**Figure 4.** Figure 4: Sensitivity analysis of manifold curvature c and balance coefficient (λ1, λ2) on the Mutagenicity dataset. More results are reported in Appendix J.2. 5.6. Sensitivity Analysis We conduct a sensitivity analysis of manifold curvature c and balance coefficient (λ1, λ2), and the results are shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Visualization of domain shifts across different types. (a) Node distribution shift between sub-datasets of PROTEINS. (b) Edge distribution shift between sub-datasets of PROTEINS. (c) Feature distribution shift between BZR and BZR MD datasets. – NCI1. The NCI1 dataset (Wale et al., 2008) consists of 4,100 molecular graphs, where nodes represent atoms and edges correspond to chemical bonds. Each graph is ann… view at source ↗

**Figure 6.** Figure 6: The performance with different GNN architectures on different datasets. 0.5 0.6 0.7 0.8 0.9 0.65 0.75 0.85 Accuracy M0 -> M1 M1 -> M0 M0 -> M2 M2 -> M0 (a) Mutagenicity 0.5 0.6 0.7 0.8 0.9 0.6 0.8 1.0 Accuracy P0 -> P1 P1 -> P0 P0 -> P2 P2 -> P0 (b) PROTEINS 0.5 0.6 0.7 0.8 0.9 0.6 0.7 0.8 0.9 Accuracy N0 -> N1 N1 -> N0 N0 -> N2 N2 -> N0 (c) NCI1 0.5 0.6 0.7 0.8 0.9 0.60 0.65 0.70 0.75 Accuracy H0 -> H1 H1… view at source ↗

**Figure 7.** Figure 7: Hyperparameter sensitivity analysis of confidence threshold ζ on the Mutagenicity, PROTEINS, NCI1 and ogbg-molhiv datasets. – GAA: GAA (Fang et al., 2025) investigates attribute-driven graph domain adaptation by leveraging node attributes to guide representation alignment across domains, demonstrating that attribute information plays a critical role in mitigating domain shifts and improving transfer perfor… view at source ↗

**Figure 8.** Figure 8: Hyperparameter sensitivity analysis of curve ratio c on the PROTEINS, NCI1 and ogbg-molhiv datasets. and geometric constraints introduce an additional term of O [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗

**Figure 9.** Figure 9: The model performance w.r.t. different combinations of λ1, λ2 and λ3. Additionally, we provide sensitivity analyses of the proposed DisRFM with respect to balance coefficient (λ1, λ3) and (λ2, λ3) on the Mutagenicity dataset. The results are illustrated in Figures 9, from which we observe trends consistent with those discussed in Section 5.6. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

read the original abstract

Graph Domain Adaptation (GDA) aims to transfer graph classifiers across domains with both semantic and topological shifts. Existing Euclidean adversarial methods face two challenges: Structural Degeneration, where domain confusion entangles and suppresses label-relevant topology, and Optimization Instability, where minimax training induces oscillatory gradients under large structural shifts. We propose DisRFM, a geometry-aware GDA framework that addresses these challenges with Riemannian representation learning and flow-based transport. DisRFM embeds graph representations on a constant-curvature manifold and expresses them in geodesic polar coordinates. Polar endpoint regularization calibrates topologysensitive radial scales via univariate Wasserstein alignment and preserves scalenormalized class semantics through confidence-filtered angular alignment, with radial magnitude modulating pseudo-label reliability. DisRFM introduces topologyconditioned polar flow matching, which couples class-compatible source and target samples by a normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis characterizes the structural risk of unconditional domain confusion and relates polar discrepancies and flow error to target risk. Extensive experiments under diverse domain shifts demonstrate that DisRFM consistently outperforms state-of-the-art methods.

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.

Desk Editor's Note private letter to a colleague

DisRFM proposes a Riemannian polar flow matching method for graph domain adaptation that targets structural preservation, but the theoretical relations need full derivation checks.

read the letter

The main point is that DisRFM embeds graph representations on constant-curvature manifolds in geodesic polar coordinates, then uses polar endpoint regularization (Wasserstein radial plus confidence-filtered angular) and topology-conditioned flow matching to align domains without the structural degeneration common in Euclidean adversarial setups. It claims this reduces optimization instability and links polar discrepancies plus flow error to target risk. The experiments reportedly show consistent gains over SOTA under various shifts, which would be useful if the ablations confirm the components matter.

Referee Report

2 major / 2 minor

Summary. The paper proposes DisRFM, a geometry-aware framework for graph domain adaptation (GDA). It embeds graph representations on a constant-curvature Riemannian manifold expressed in geodesic polar coordinates, applies polar endpoint regularization (Wasserstein radial alignment plus confidence-filtered angular alignment, with radial magnitude modulating pseudo-label reliability), and introduces topology-conditioned polar flow matching that couples class-compatible samples via normalized polar transport cost and learns a metric-corrected vector field along geodesic interpolants. Theoretical analysis characterizes structural risk under unconditional domain confusion and relates polar discrepancies plus flow error to target risk. Experiments under diverse domain shifts claim consistent outperformance over state-of-the-art methods by mitigating structural degeneration and optimization instability.

Significance. If the theoretical relations and empirical gains hold, the work would advance GDA by supplying a structure-preserving alternative to Euclidean adversarial methods through Riemannian geometry and flow-based transport. Strengths include the explicit coupling of geometry (polar coordinates, constant-curvature embedding) with flow matching and the attempt to derive risk bounds from polar discrepancies. The framework's focus on topology-sensitive regularization and metric-corrected vector fields offers a coherent path to more stable adaptation under topological shifts.

major comments (2)

[Theoretical analysis] Theoretical analysis: the stated relations between polar discrepancies, flow error, and target risk are presented as characterizing structural risk, but the manuscript must supply the explicit derivation or bounding steps (e.g., how the normalized polar transport cost enters the target-risk bound) for this link to support the central claim of structure preservation.
[Experiments] Experiments: the claim of consistent outperformance requires ablation tables isolating the contribution of polar endpoint regularization versus the flow-matching component, together with statistical significance tests across the reported domain-shift settings; without these, the attribution to Riemannian polar coordinates remains unverified.

minor comments (2)

[Method] Clarify the precise definition of the 'normalized polar transport cost' and the radial-scale calibration weights early in the method section to avoid ambiguity in the flow-matching objective.
[Figures] Figure captions should explicitly state the manifold curvature value and radial-scale calibration procedure used for each plotted result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and have revised the manuscript to strengthen the presentation of the theoretical relations and experimental validation.

read point-by-point responses

Referee: [Theoretical analysis] Theoretical analysis: the stated relations between polar discrepancies, flow error, and target risk are presented as characterizing structural risk, but the manuscript must supply the explicit derivation or bounding steps (e.g., how the normalized polar transport cost enters the target-risk bound) for this link to support the central claim of structure preservation.

Authors: We agree that the original manuscript presented the relations at a high level without fully expanded bounding steps. In the revised version we have inserted a complete derivation in Section 4 (Theorem 2 and its proof), explicitly showing the application of the triangle inequality on the geodesic distance, the decomposition of the normalized polar transport cost into radial and angular components, and the subsequent bounding of the target risk by the sum of the polar discrepancy term and the flow-matching error. This makes the structure-preservation claim fully rigorous. revision: yes
Referee: [Experiments] Experiments: the claim of consistent outperformance requires ablation tables isolating the contribution of polar endpoint regularization versus the flow-matching component, together with statistical significance tests across the reported domain-shift settings; without these, the attribution to Riemannian polar coordinates remains unverified.

Authors: We acknowledge that the original experiments lacked component-wise ablations and statistical tests. The revised manuscript now includes new ablation tables (Table 5 and Table 6) that separately disable polar endpoint regularization and the topology-conditioned flow-matching module, together with paired t-test p-values computed across all domain-shift configurations. These additions confirm that both components contribute measurably to the observed gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper proposes a new GDA framework using constant-curvature Riemannian embeddings in geodesic polar coordinates, followed by Wasserstein-based polar regularization and topology-conditioned flow matching. The theoretical analysis relates polar discrepancies and flow error to target risk without reducing any claimed prediction or first-principles result to a fitted parameter or self-defined quantity by construction. No load-bearing self-citation chains, ansatz smuggling, or renaming of known results as novel derivations are present. The central claims rest on standard Riemannian geometry and optimal transport applied to graph data, with independent empirical validation under domain shifts.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumption that constant-curvature manifolds and polar coordinates can separate topology-sensitive radial scales from class semantics without loss; several alignment steps introduce tunable elements whose values are not derived from first principles.

free parameters (2)

manifold curvature
Constant-curvature value must be chosen or fitted for the embedding step.
radial scale calibration weights
Univariate Wasserstein alignment parameters that calibrate topologically sensitive scales.

axioms (2)

domain assumption Graph representations admit faithful embedding on a constant-curvature manifold that preserves label-relevant topology.
Invoked when moving from Euclidean to Riemannian representation learning.
domain assumption Geodesic polar coordinates cleanly separate radial magnitude (topology) from angular direction (semantics).
Central premise of the polar endpoint regularization and flow construction.

invented entities (1)

topology-conditioned polar flow matching no independent evidence
purpose: Couples source and target samples via normalized polar transport cost and learns a metric-corrected vector field.
New transport mechanism introduced to replace standard Euclidean flow or adversarial objectives.

pith-pipeline@v0.9.0 · 5506 in / 1495 out tokens · 56707 ms · 2026-05-16T09:02:11.974369+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel; dAlembert_cosh_solution_aczel echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

Hyperbolic (H, c <0 ):The volume expands exponentially, satisfying: lim R→∞ Vol(BH(R))/exp((d−1)√|c|R) =const>0. ... Theorem 4.2 ... gradient flows for structural preservation (∇rL) and semantic alignment (∇θL) are orthogonal under the Riemannian metric: ⟨∇rL,∇θL⟩g=0.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking; SphereAdmitsCircleLinking echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

we embed graphs into a Riemannian manifold. By adopting polar coordinates, we explicitly disentangle structure (radius) from semantics (angle). ... flow matching ... along geodesic paths

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

DSBD: Dual-Aligned Structural Basis Distillation for Graph Domain Adaptation
cs.LG 2026-04 unverdicted novelty 7.0

DSBD distills a dual-aligned structural basis to adapt GNNs across graphs with structural distribution shifts, outperforming prior methods on benchmarks.
When Brain Networks Travel: Learning Beyond Site
cs.LG 2026-05 unverdicted novelty 5.0

CORE decouples site confounders in fMRI networks, profiles transient dynamics on a population scaffold using line graphs, and applies subject-adaptive gating to achieve up to 6.7% better cross-site generalization on A...

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · cited by 2 Pith papers · 4 internal anchors

[1]

Domain-Adversarial Neural Networks

Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., and Marchand, M. Domain-adversarial neural networks. arXiv preprint arXiv:1412.4446,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

Baek, J., Kang, M., and Hwang, S. J. Accurate learning of graph representations with graph multiset pooling.arXiv preprint arXiv:2102.11533,

work page arXiv
[3]

Borde, H. S. d. O., Kazi, A., Barbero, F., and Li`o, P. Latent graph inference using product manifolds.arXiv preprint arXiv:2211.16199,

work page arXiv
[4]

Graffe: Graph representation learning via diffusion probabilistic models.arXiv preprint arXiv:2505.04956, 2025a

Chen, D., Xue, S., Chen, L., Wang, Y ., Liu, Q., Wu, S., Ma, Z.-M., and Wang, L. Graffe: Graph representation learning via diffusion probabilistic models.arXiv preprint arXiv:2505.04956, 2025a. Chen, W., Ye, G., Wang, Y ., Zhang, Z., Zhang, L., Wang, D., Zhang, Z., and Zhuang, F. Smoothness really matters: A simple yet effective approach for unsupervised ...

work page arXiv
[5]

H., Pu, R., Wang, B., and Ling, C

Fang, R., Li, B., Kang, Z., Zeng, Q., Dashtbayaz, N. H., Pu, R., Wang, B., and Ling, C. On the benefits of attribute-driven graph domain adaptation.arXiv preprint arXiv:2502.06808,

work page arXiv
[6]

Geometric mo- ment alignment for domain adaptation via siegel embed- dings.arXiv preprint arXiv:2510.14666,

Gharib, S., Hartmann, M., and Klami, A. Geometric mo- ment alignment for domain adaptation via siegel embed- dings.arXiv preprint arXiv:2510.14666,

work page arXiv
[7]

arXiv preprint arXiv:2103.09430 (2021)

Hu, W., Fey, M., Ren, H., Nakata, M., Dong, Y ., and Leskovec, J. Ogb-lsc: A large-scale challenge for machine learning on graphs.arXiv preprint arXiv:2103.09430,

work page arXiv
[8]

Graph generation with spectral geodesic flow matching.arXiv preprint arXiv:2510.02520,

Huang, X., Ruan, T., Zhang, C., and Zhang, S. Graph generation with spectral geodesic flow matching.arXiv preprint arXiv:2510.02520,

work page arXiv
[9]

J., O’brien, L

Sutherland, J. J., O’brien, L. A., and Weaver, D. F. Spline- fitting with a genetic algorithm: A method for developing classification structure- activity relationships.Journal of chemical information and computer sciences, 43(6): 1906–1915,

work page 1906
[10]

Poincar\'e GloVe: Hyperbolic Word Embeddings

Tifrea, A., B ´ecigneul, G., and Ganea, O.-E. Poincar \’e glove: Hyperbolic word embeddings.arXiv preprint arXiv:1810.06546,

work page internal anchor Pith review Pith/arXiv arXiv
[11]

Improving and generalizing flow-based generative models with minibatch optimal transport

Tong, A., Malkin, N., Huguet, G., Zhang, Y ., Rector-Brooks, J., Fatras, K., Wolf, G., and Bengio, Y . Conditional flow matching: Simulation-free dynamic optimal transport. arXiv preprint arXiv:2302.00482, 2(3),

work page internal anchor Pith review Pith/arXiv arXiv
[12]

Dgnn: Decoupled graph neural networks with structural consistency between attribute and graph embedding representations.IEEE Transactions on Big Data, 2024a

Wang, J., Guo, J., Sun, Y ., Gao, J., Wang, S., Yang, Y ., and Yin, B. Dgnn: Decoupled graph neural networks with structural consistency between attribute and graph embedding representations.IEEE Transactions on Big Data, 2024a. Wang, Y ., Wang, M., Su, H., Yin, N., Yao, Q., and Kwok, J. Degree-conscious spiking graph for cross-domain adapta- tion.arXiv p...

work page arXiv
[13]

Graph learning under distribution shifts: A comprehensive survey on domain adaptation, out- of-distribution, and continual learning.arXiv preprint arXiv:2402.16374,

Wu, M., Zheng, X., Zhang, Q., Shen, X., Luo, X., Zhu, X., and Pan, S. Graph learning under distribution shifts: A comprehensive survey on domain adaptation, out- of-distribution, and continual learning.arXiv preprint arXiv:2402.16374,

work page arXiv
[14]

How Powerful are Graph Neural Networks?

Xu, K., Hu, W., Leskovec, J., and Jegelka, S. How powerful are graph neural networks?arXiv preprint arXiv:1810.00826,

work page internal anchor Pith review Pith/arXiv arXiv
[15]

Dream: A dual variational framework for unsupervised graph domain adaptation.IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(11):10787–10800, 2025a

Yin, N., Shen, L., Wang, M., Liu, X., Chen, C., and Hua, X.- S. Dream: A dual variational framework for unsupervised graph domain adaptation.IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(11):10787–10800, 2025a. doi: 10.1109/TPAMI.2025.3596054. Yin, N., Shen, L., Wang, M., Liu, X., Chen, C., and Hua, X.- S. Dream: a dual variational fr...

work page doi:10.1109/tpami.2025.3596054 2025
[16]

In dynamical systems, a vector field F is conservative if it can be expressed as the gradient of a scalar potential, i.e., F=−∇Φ

if and only if ∥∇θLF M∥= 0 , which corresponds to the critical points (stationary points) of the loss landscape. In dynamical systems, a vector field F is conservative if it can be expressed as the gradient of a scalar potential, i.e., F=−∇Φ. • DisRFM:The update field is FF M =−∇L F M. It is strictly conservative. The system cannot return to a previous st...

work page 2002
[17]

Let H be a hypothesis space

and decompose the realized divergence term into geometric and optimization components to demonstrate the superiority of our framework. Let H be a hypothesis space. For any hypothesis h∈ H , let ϵS(h) and ϵT (h) be the risks on the source and target domains, respectively. The standard bound is given by: ϵT (h)≤ϵ S(h) + 1 2 ˆdH∆H(DS,D T ) +C,(40) where ˆdH∆...

work page 2011
[18]

is a motif-aware Riemannian graph neural network that leverages gen- erative–contrastive learning to capture higher-order structural patterns and geometric relationships in graph representations. •Graph Domain Adaptation method.We compare DisRFM with seven graph domain adaptation methods: – DEAL: DEAL (Yin et al., 2022): addresses unsupervised domain adap...

work page 2022
[19]

performs domain adaptation by aligning geometric moments via Siegel embeddings, enabling principled matching of higher-order distributional statistics across domains in a structured geometric space. H.1. Implmentation Details We implement all baselines and conduct all experiments on NVIDIA A100 GPUs to ensure fair comparison. All methods are evaluated und...

work page 2020

[1] [1]

Domain-Adversarial Neural Networks

Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., and Marchand, M. Domain-adversarial neural networks. arXiv preprint arXiv:1412.4446,

work page internal anchor Pith review Pith/arXiv arXiv

[2] [2]

Baek, J., Kang, M., and Hwang, S. J. Accurate learning of graph representations with graph multiset pooling.arXiv preprint arXiv:2102.11533,

work page arXiv

[3] [3]

Borde, H. S. d. O., Kazi, A., Barbero, F., and Li`o, P. Latent graph inference using product manifolds.arXiv preprint arXiv:2211.16199,

work page arXiv

[4] [4]

Graffe: Graph representation learning via diffusion probabilistic models.arXiv preprint arXiv:2505.04956, 2025a

Chen, D., Xue, S., Chen, L., Wang, Y ., Liu, Q., Wu, S., Ma, Z.-M., and Wang, L. Graffe: Graph representation learning via diffusion probabilistic models.arXiv preprint arXiv:2505.04956, 2025a. Chen, W., Ye, G., Wang, Y ., Zhang, Z., Zhang, L., Wang, D., Zhang, Z., and Zhuang, F. Smoothness really matters: A simple yet effective approach for unsupervised ...

work page arXiv

[5] [5]

H., Pu, R., Wang, B., and Ling, C

Fang, R., Li, B., Kang, Z., Zeng, Q., Dashtbayaz, N. H., Pu, R., Wang, B., and Ling, C. On the benefits of attribute-driven graph domain adaptation.arXiv preprint arXiv:2502.06808,

work page arXiv

[6] [6]

Geometric mo- ment alignment for domain adaptation via siegel embed- dings.arXiv preprint arXiv:2510.14666,

Gharib, S., Hartmann, M., and Klami, A. Geometric mo- ment alignment for domain adaptation via siegel embed- dings.arXiv preprint arXiv:2510.14666,

work page arXiv

[7] [7]

arXiv preprint arXiv:2103.09430 (2021)

Hu, W., Fey, M., Ren, H., Nakata, M., Dong, Y ., and Leskovec, J. Ogb-lsc: A large-scale challenge for machine learning on graphs.arXiv preprint arXiv:2103.09430,

work page arXiv

[8] [8]

Graph generation with spectral geodesic flow matching.arXiv preprint arXiv:2510.02520,

Huang, X., Ruan, T., Zhang, C., and Zhang, S. Graph generation with spectral geodesic flow matching.arXiv preprint arXiv:2510.02520,

work page arXiv

[9] [9]

J., O’brien, L

Sutherland, J. J., O’brien, L. A., and Weaver, D. F. Spline- fitting with a genetic algorithm: A method for developing classification structure- activity relationships.Journal of chemical information and computer sciences, 43(6): 1906–1915,

work page 1906

[10] [10]

Poincar\'e GloVe: Hyperbolic Word Embeddings

Tifrea, A., B ´ecigneul, G., and Ganea, O.-E. Poincar \’e glove: Hyperbolic word embeddings.arXiv preprint arXiv:1810.06546,

work page internal anchor Pith review Pith/arXiv arXiv

[11] [11]

Improving and generalizing flow-based generative models with minibatch optimal transport

Tong, A., Malkin, N., Huguet, G., Zhang, Y ., Rector-Brooks, J., Fatras, K., Wolf, G., and Bengio, Y . Conditional flow matching: Simulation-free dynamic optimal transport. arXiv preprint arXiv:2302.00482, 2(3),

work page internal anchor Pith review Pith/arXiv arXiv

[12] [12]

Dgnn: Decoupled graph neural networks with structural consistency between attribute and graph embedding representations.IEEE Transactions on Big Data, 2024a

Wang, J., Guo, J., Sun, Y ., Gao, J., Wang, S., Yang, Y ., and Yin, B. Dgnn: Decoupled graph neural networks with structural consistency between attribute and graph embedding representations.IEEE Transactions on Big Data, 2024a. Wang, Y ., Wang, M., Su, H., Yin, N., Yao, Q., and Kwok, J. Degree-conscious spiking graph for cross-domain adapta- tion.arXiv p...

work page arXiv

[13] [13]

Graph learning under distribution shifts: A comprehensive survey on domain adaptation, out- of-distribution, and continual learning.arXiv preprint arXiv:2402.16374,

Wu, M., Zheng, X., Zhang, Q., Shen, X., Luo, X., Zhu, X., and Pan, S. Graph learning under distribution shifts: A comprehensive survey on domain adaptation, out- of-distribution, and continual learning.arXiv preprint arXiv:2402.16374,

work page arXiv

[14] [14]

How Powerful are Graph Neural Networks?

Xu, K., Hu, W., Leskovec, J., and Jegelka, S. How powerful are graph neural networks?arXiv preprint arXiv:1810.00826,

work page internal anchor Pith review Pith/arXiv arXiv

[15] [15]

Dream: A dual variational framework for unsupervised graph domain adaptation.IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(11):10787–10800, 2025a

Yin, N., Shen, L., Wang, M., Liu, X., Chen, C., and Hua, X.- S. Dream: A dual variational framework for unsupervised graph domain adaptation.IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(11):10787–10800, 2025a. doi: 10.1109/TPAMI.2025.3596054. Yin, N., Shen, L., Wang, M., Liu, X., Chen, C., and Hua, X.- S. Dream: a dual variational fr...

work page doi:10.1109/tpami.2025.3596054 2025

[16] [16]

In dynamical systems, a vector field F is conservative if it can be expressed as the gradient of a scalar potential, i.e., F=−∇Φ

if and only if ∥∇θLF M∥= 0 , which corresponds to the critical points (stationary points) of the loss landscape. In dynamical systems, a vector field F is conservative if it can be expressed as the gradient of a scalar potential, i.e., F=−∇Φ. • DisRFM:The update field is FF M =−∇L F M. It is strictly conservative. The system cannot return to a previous st...

work page 2002

[17] [17]

Let H be a hypothesis space

and decompose the realized divergence term into geometric and optimization components to demonstrate the superiority of our framework. Let H be a hypothesis space. For any hypothesis h∈ H , let ϵS(h) and ϵT (h) be the risks on the source and target domains, respectively. The standard bound is given by: ϵT (h)≤ϵ S(h) + 1 2 ˆdH∆H(DS,D T ) +C,(40) where ˆdH∆...

work page 2011

[18] [18]

is a motif-aware Riemannian graph neural network that leverages gen- erative–contrastive learning to capture higher-order structural patterns and geometric relationships in graph representations. •Graph Domain Adaptation method.We compare DisRFM with seven graph domain adaptation methods: – DEAL: DEAL (Yin et al., 2022): addresses unsupervised domain adap...

work page 2022

[19] [19]

performs domain adaptation by aligning geometric moments via Siegel embeddings, enabling principled matching of higher-order distributional statistics across domains in a structured geometric space. H.1. Implmentation Details We implement all baselines and conduct all experiments on NVIDIA A100 GPUs to ensure fair comparison. All methods are evaluated und...

work page 2020