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
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 ± 0.20
62.45 ± 1.16
86.44 ± 0.44
87.72 ± 1.35
91.26 ± 1.15
61.39 ± 2.96
48.59 ± 4.52
62.00 ± 0.24
HyperGCN ( Yadati et al., 2019 )
89.98 ± 0.43
72.76 ± 1.12
82.84 ± 0.67
86.36 ± 1.86
87.43 ± 1.46
60.13 ± 1.76
50.13 ± 3.21
48.74 ± 2.81
HNHN ( Dong et al., 2020 )
86.78 ± 0.29
72.64 ± 1.57
84.21 ± 0.64
86.13 ± 0.76
90.89 ± 0.31
67.80 ± 2.59
50.93 ± 6.33
51.18 ± 0.35
HCHA ( Bai et al., 2021 )
90.92 ± 0.22
72.42 ± 1.42
84.56 ± 0.31
87.12 ± 1.23
90.43 ± 1.20
61.36 ± 2.53
48.62 ± 4.41
62.35 ± 0.26
UniGCNII ( Huang and Yang, 2021 )
91.69 ± 0.19
73.05 ± 2.21
87.31 ± 0.45
89.30 ± 1.33
92.43 ± 0.71
67.25 ± 2.57
49.30 ± 4.25
54.45 ± 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
74.56±1.16
84.78±1.57
77.18±2.35
76.06±4.13
γ0,β0 , μ0
73.67±0.96
83.36±1.23
75.73±1.79
75.13±2.17
γv=0
71.15±1.58
82.11±1.34
72.27±2.34
71.19±3.16
βv=0
66.46±1.17
81.41±1.18
65.79±3.78
62.17±0.89
μ=0
72.46±1.67
82.43±1.07
74.28±2.79
75.23±2.17
γv,βv,μ=0
63.04±1.72
79.16±1.96
62.16±2.36
50.89±3.36
Table 3. Ablation Study
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Notation
Description
M
A Riemannian manifold
hM
The Cheeger’s constant of M
ξ
A small value variable
ε(⋅)
The radius function
λi,ψi
The i -th eigenvalue and eigenfunction of the Laplace-Beltrami operator.
∂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.
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.
Mengyao Zhou, Zhiheng Zhou, Xiao Han +3
the Academy of Mathematics and Systems Science, Chinese Academy of Sciences and also with the University of Chinese Academy of Sciences, Beijing 100190, China · the School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China · School of Artificial Intelligence, Beihang University, Beijing 100191, China +1
Hypergraph knowledge distillation aims to retain the predictive performance of a hypergraph neural network (HNN) teacher while reducing inference costs through a lightweight student model. In this work, we observe that HNNs exhibit substantially lower prediction performance on heterophilic nodes connected through semantically diverse hyperedges, indicating that the reliability of teacher knowledge varies across nodes. Motivated by this observation, we propose HADES, a heterophily-aware adaptive distillation method for hypergraph neural networks. HADES quantifies node heterophily and leverages it as an estimate of teacher reliability to modulate the transfer of teacher knowledge during distillation. Experimental results on real-world hypergraphs demonstrate that HADES consistently improves student performance across different HNN teachers and distillation objectives. In many cases, the resulting student models surpass the predictive performance of their teachers while achieving up to 12.3 times faster inference.
Joohee Cho, David Yoon Suk Kang, Yunyong Ko
Chung-Ang University · Seoul, South Korea · Chungbuk National University +1
Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.
Zhiheng Zhou, Mengyao Zhou, Yancheng Chen +3
School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China · Academy of Mathematics and Systems Science, Chinese Academy of Sciences and also with the University of Chinese Academy of Sciences, Beijing 100190, China