Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger

Li Sun; Ming Zhang; Wenxin Jin; Zhongtian Sun; Zhenhao Huang; Hao Peng; Sen Su; Philip Yu

cs.AIFeb 28, 2026

Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger

Authors: Li Sun, Ming Zhang, Wenxin Jin, Zhongtian Sun, Zhenhao Huang, Hao Peng, Sen Su, Philip Yu

Organizations: Beijing University of Posts and Telecommunications, Beijing, China · North China Electric Power University, Beijing, China · University of Kent, Canterbury, United Kingdom · Beihang University, Beijing, China · University of Illinois, Chicgao, United States

Abstract

Hypergraphs are the natural description of higher-order interactions among objects, widely applied in social network analysis, cross-modal retrieval, etc. Hypergraph Neural Networks (HGNNs) have become the dominant solution for learning on hypergraphs. Traditional HGNNs are extended from message passing graph neural networks, following the homophily assumption, and thus struggle with the prevalent heterophilic hypergraphs that call for long-range dependence modeling. In this paper, we achieve heterophily-agnostic message passing through the lens of Riemannian geometry. The key insight lies in the connection between oversquashing and hypergraph bottleneck within the framework of Riemannian manifold heat flow. Building on this, we propose the novel idea of locally adapting the bottlenecks of different subhypergraphs. The core innovation of the proposed mechanism is the design of an adaptive local (heat) exchanger. Specifically, it captures the rich long-range dependencies via the Robin condition, and preserves the representation distinguishability via source terms, thereby enabling heterophily-agnostic message passing with theoretical guarantees. Based on this theoretical foundation, we present a novel Heat-Exchanger with Adaptive Locality for Hypergraph Neural Network (HealHGNN), designed as a node-hyperedge bidirectional systems with linear complexity in the number of nodes and hyperedges. Extensive experiments on both homophilic and heterophilic cases show that HealHGNN achieves the state-of-the-art performance.

Figures & tables

Figure 1. (A). Traditional dynamics in HGNN. (B). Illustration of our adaptive heat exchanger; bd denotes boundary nodes.

Figure 2. Overall architecture of the proposed heat kernel based hypergraph neural network.

Type	Homophilic hypergraphs				Heterophilic hypergraphs
Dataset	DBLP-CA	Citeseer	Pubmed	NTU2012	Congress	House	Senate	Walmart
HGNN ( Feng et al., 2019 )	91.03 $\pm$ 0.20	62.45 $\pm$ 1.16	86.44 $\pm$ 0.44	87.72 $\pm$ 1.35	91.26 $\pm$ 1.15	61.39 $\pm$ 2.96	48.59 $\pm$ 4.52	62.00 $\pm$ 0.24
HyperGCN ( Yadati et al., 2019 )	89.98 $\pm$ 0.43	72.76 $\pm$ 1.12	82.84 $\pm$ 0.67	86.36 $\pm$ 1.86	87.43 $\pm$ 1.46	60.13 $\pm$ 1.76	50.13 $\pm$ 3.21	48.74 $\pm$ 2.81
HNHN ( Dong et al., 2020 )	86.78 $\pm$ 0.29	72.64 $\pm$ 1.57	84.21 $\pm$ 0.64	86.13 $\pm$ 0.76	90.89 $\pm$ 0.31	67.80 $\pm$ 2.59	50.93 $\pm$ 6.33	51.18 $\pm$ 0.35
HCHA ( Bai et al., 2021 )	90.92 $\pm$ 0.22	72.42 $\pm$ 1.42	84.56 $\pm$ 0.31	87.12 $\pm$ 1.23	90.43 $\pm$ 1.20	61.36 $\pm$ 2.53	48.62 $\pm$ 4.41	62.35 $\pm$ 0.26
UniGCNII ( Huang and Yang, 2021 )	91.69 $\pm$ 0.19	73.05 $\pm$ 2.21	87.31 $\pm$ 0.45	89.30 $\pm$ 1.33	92.43 $\pm$ 0.71	67.25 $\pm$ 2.57	49.30 $\pm$ 4.25	54.45 $\pm$ 0.37

Table 1. Node classification on homophilic and heterophilic hypergraphs. Top three models are coloured by First , Second , Third .

	Heterophily Level
Methods	1	2	3	4	5	6	7
HGNN	97.8	85.7	78.4	70.5	66.5	64.9	60.4
HyperGCN	85.1	77.1	75.9	72.9	69.5	65.1	60.7
HCHA	98.4	83.8	79.3	74.1	72.1	69.1	64.3
AllDeepSets	99.8	87.8	82.4	77.3	73.4	71.8	68.4
AllSetTransformer	99.9	86.5	83.3	78.5	74.2	72.4	69.2

Table 2. Heterophily Experiments

Figure 3. Illustration of the Topological Structures

Figure 4. Performance comparison on LRGB tasks.

Figure 5. Information Transfer Performance on the Four Hypergraph Types with Hyperedge Size 4.

Figure 6. Comparison of method performance across varying neural network depths on four datasets.

Model	Citeseer	Cora-CA	House	Senate
HealHGNN	$\mathbf{74.56}{\scriptstyle\pm 1.16}$	$\mathbf{84.78}{\scriptstyle\pm 1.57}$	$\mathbf{77.18}{\scriptstyle\pm 2.35}$	$\mathbf{76.06}{\scriptstyle\pm 4.13}$
$\gamma_{0},\beta_{0}$ , $\mu_{0}$	$73.67{\scriptstyle\pm 0.96}$	$83.36{\scriptstyle\pm 1.23}$	$75.73{\scriptstyle\pm 1.79}$	$75.13{\scriptstyle\pm 2.17}$
$\gamma_{v}=0$	$71.15{\scriptstyle\pm 1.58}$	$82.11{\scriptstyle\pm 1.34}$	$72.27{\scriptstyle\pm 2.34}$	$71.19{\scriptstyle\pm 3.16}$
$\beta_{v}=0$	$66.46{\scriptstyle\pm 1.17}$	$81.41{\scriptstyle\pm 1.18}$	$65.79{\scriptstyle\pm 3.78}$	$62.17{\scriptstyle\pm 0.89}$
$\mu=0$	$72.46{\scriptstyle\pm 1.67}$	$82.43{\scriptstyle\pm 1.07}$	$74.28{\scriptstyle\pm 2.79}$	$75.23{\scriptstyle\pm 2.17}$
$\gamma_{v},\beta_{v},\mu=0$	$63.04{\scriptstyle\pm 1.72}$	$79.16{\scriptstyle\pm 1.96}$	$62.16{\scriptstyle\pm 2.36}$	$50.89{\scriptstyle\pm 3.36}$

Table 3. Ablation Study

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Notation	Description
$\mathcal{M}$	A Riemannian manifold
$h_{\mathcal{M}}$	The Cheeger’s constant of $\mathcal{M}$
$\xi$	A small value variable
$\varepsilon(\cdot)$	The radius function
$\lambda_{i},\psi_{i}$	The $i$ -th eigenvalue and eigenfunction of the Laplace-Beltrami operator.
$\partial_{t}$	The parital derivative w.r.t. $t$

Appendix

Table 4. Notations.

Dataset	n_layer	hid_dim	tau	dropout	lr	w_decay
Cora-CA	3	128	0.001	0.7	5e-05	5e-07
DBLP-CA	5	128	0.01	0.7	1e-03	0.0
Citeseer	3	512	0.1	0.8	5e-03	5e-05
Pubmed	3	64	0.5	0.6	5e-03	5e-05
Congress	5	512	0.1	0.35	5e-03	0.0
House	5	512	0.5	0.35	3e-04	0.0

Appendix

Table 5. Hyperparameter settings for node classification task.

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Hypergraph Neural Networks Hypergraph Learning Graph Neural Networks Graph Diffusion

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Hypergraph neural networks (HGNNs) have demonstrated strong capabilities in modeling complex higher-order relationships. However, existing HGNNs often suffer from over-smoothing as the number of layers increases and lack effective control over message passing among nodes. Inspired by the theory of Ricci flow in differential geometry, we theoretically establish that introducing discrete Ricci flow into hypergraph structures can effectively regulate node feature evolution and thereby alleviate over-smoothing. Building on this insight, we propose Ricci Flow-guided Hypergraph Neural Diffusion(RFHND), a novel message passing paradigm for hypergraphs guided by discrete Ricci flow. Specifically, RFHND is based on a PDE system that describes the continuous evolution of node features on hypergraphs and adaptively regulates the rate of information diffusion at the geometric level, preventing feature homogenization and producing high-quality node representations. Experimental results show that RFHND significantly outperforms existing methods across multiple benchmark datasets and demonstrates strong robustness, while also effectively mitigating over-smoothing.

Abstract

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