Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphs
Abstract
Graph Neural Networks (GNNs) have gained significant attention as a powerful modeling and inference method, especially for homophilic graph-structured data. To empower GNNs in heterophilic graphs, where adjacent nodes exhibit dissimilar labels or features, Signed Message Passing (SMP) has been widely adopted. However, there is a lack of theoretical and empirical analysis regarding the limitations of SMP. In this work, we unveil some potential pitfalls of SMP and their remedies. We first identify two limitations of SMP: undesirable representation update for multi-hop neighbors and vulnerability against oversmoothing issues. To overcome these challenges, we propose a novel message passing function called Multiset to Multiset GNN(M2M-GNN). Our theoretical analyses and extensive experiments demonstrate that M2M-GNN effectively alleviates the aforementioned limitations of SMP, yielding superior performance in comparison
Benchmark Results
Tested on 6 datasets 28 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9672
±0.0147 | |
| 2 | DoG | 0.9660
±0.0210 | |
| 3 | GPF-plus | 0.9583
±0.0419 | |
| 5 | ACM-GCN | 0.9557
±0.0360 best reported | best at pub: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 30 | GPR-GNN | 0.9291
±0.0132 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) |
| 34 | MLP | 0.9230
±0.0070 best reported | |
| 39 | GGCN | 0.9213
±0.0305 best reported | best at pub: Understanding convolution on graphs via energies (TMLR 2022) best today: Graph Wave Networks (WWW 2025) |
| 40 | H2GCN | 0.9189
±0.0393 best reported | best at pub: LOGIN: A Large Language Model Consulted Graph Neural Network Training Framework (2024) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) Difference within reported uncertainty; not counted as underperformance. |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 61 | FAGCN | 0.8961
±0.0152 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 69 | M2M-GNN | 0.8919
±0.0450 | This paper |
| 68 | DMP | 0.8919 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 114 | Ord. GNN | 0.8622
±0.0410 | This paper |
| 164 | AERO-GNN | 0.8435
±0.0520 | This paper |
| 175 | GOAL | 0.8362
±0.0670 | Improvement within reported uncertainty; not highlighted. |
| 211 | GAT | 0.8162
±0.0645 best reported | best at pub: A Quasi-Wasserstein Loss for Learning Graph Neural Networks (WWW 2023) best today: Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (2025) |
| 257 | GCN | 0.7933
±0.0447 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Graph Wave Networks (WWW 2025) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9541
±0.0272 | |
| 2 | ACM-GCN | 0.9480
±0.0380 best reported | best at pub: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) best today: Heterophily-informed Message Passing (TMLR 2025) |
| 3 | RF-GCN | 0.9429 | |
| 11 | GPR-GNN | 0.9279
±0.0312 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 15 | GGCN | 0.9230
±0.0367 best reported | best at pub: Understanding convolution on graphs via energies (TMLR 2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 24 | MLP | 0.9136
±0.0070 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) Difference within reported uncertainty; not counted as underperformance. |
| 31 | DMP | 0.8919 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 38 | FAGCN | 0.8852
±0.0133 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 53 | Ord. GNN | 0.8703
±0.0470 | This paper |
| 64 | M2M-GNN | 0.8648
±0.0610 | This paper |
| 68 | H2GCN | 0.8623
±0.0471 best reported | best at pub: Design your own universe: a physics-informed agnostic method for enhancing graph neural networks (2024) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 81 | GOAL | 0.8568
±0.0620 | |
| 98 | AERO-GNN | 0.8480
±0.0330 | prev best: Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification (2023) Improvement within reported uncertainty; not highlighted. |
| 138 | SAGE | 0.8269 | |
| 158 | GAT | 0.8190
±0.0540 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 170 | GCN | 0.8082
±0.0360 best reported | best at pub: Differentiable Cluster Graph Neural Network (2024) best today: Bayesian Neighborhood Adaptation for Graph Neural Networks (TMLR 2025) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DiGGR | 0.4535
±0.0353 | |
| 2 | TRIGON | 0.4402
±0.0028 | |
| 3 | DoG | 0.4320
±0.0120 | |
| 16 | ACM-GCN | 0.4198
±0.0089 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 42 | MLP | 0.4026
±0.0108 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 53 | GPR-GNN | 0.3992
±0.0067 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) best today: Piecewise Constant Spectral Graph Neural Network (TMLR 2025) |
| 56 | FAGCN | 0.3970 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 62 | GGCN | 0.3929
±0.0048 best reported | best at pub: Feature Transportation Improves Graph Neural Networks (AAAI 2023) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 68 | GraphSAGE | 0.3899
±0.0085 | |
| 71 | H2GCN | 0.3885
±0.0117 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 92 | Ord. GNN | 0.3799
±0.0100 | This paper |
| 122 | DMP | 0.3726
±0.0179 best reported | best at pub: Heterophily-Aware Graph Attention Network (2023) |
| 135 | GCN | 0.3690 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 147 | M2M-GNN | 0.3672
±0.0160 | This paper |
| 157 | AERO-GNN | 0.3657
±0.0110 | This paper |
| 163 | GOAL | 0.3646
±0.0100 | Improvement within reported uncertainty; not highlighted. |
| 182 | GAT | 0.3605
±0.0035 best reported | best at pub: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DMD++ | 0.9190
±0.0260 | |
| 2 | F-GREAD-BS | 0.9059
±0.0380 | |
| 3 | APPNP | 0.9010
±0.0350 | |
| 11 | M2M-GNN | 0.8901
±0.0410 | This paper |
| 15 | ACM-GCN | 0.8843
±0.0320 | This paper |
| 20 | Ord. GNN | 0.8804
±0.0360 | This paper |
| 22 | H2GCN | 0.8790
±0.0420 best reported | best at pub: Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND (ICLR 2024) best today: When Graph Neural Networks Meet Dynamic Mode Decomposition (ICLR 2024) Difference within reported uncertainty; not counted as underperformance. |
| 30 | GOAL | 0.8698
±0.0440 | This paper |
| 32 | GGCN | 0.8686
±0.0320 | This paper |
| 37 | MLP | 0.8629
±0.0450 best reported | best at pub: Is Homophily a Necessity for Graph Neural Networks? (ICLR 2021) Difference within reported uncertainty; not counted as underperformance. |
| 53 | GAT | 0.8430
±0.0370 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 56 | GPR-GNN | 0.8412 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 60 | FAGCN | 0.8333 best reported | best at pub: Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating (AAAI 2022) Difference within reported uncertainty; not counted as underperformance. |
| 63 | GCN | 0.8310
±0.0320 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 68 | AERO-GNN | 0.8124
±0.0680 | This paper |
| 69 | GraphSAGE | 0.8118
±0.0556 | |
| 183 | DMP | 0.5641
±0.0550 | This paper |
Heterophily Benchmark
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | UniGAP | 0.6375
±0.0110 | |
| 2 | H2GCN + HalfHop | 0.5961
±0.0100 | |
| 3 | GraphSAGE + HalfHop | 0.5897
±0.0150 | |
| 7 | H2GCN | 0.5681
±0.0090 best reported | |
| 12 | SAGE | 0.5569
±0.0023 | |
| 14 | GAT | 0.5559
±0.0027 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) |
| 24 | GCN | 0.5411
±0.0034 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) |
| 47 | ACM-GCN | 0.5294
±0.0023 best reported | best at pub: Graph Neural Networks for Graphs with Heterophily: A Survey (2022) |
| 84 | MLP | 0.5058 best reported | best at pub: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 103 | GPR-GNN | 0.4937
±0.0071 best reported | best at pub: Evolving Computation Graphs (ICML 2023) best today: Piecewise Constant Spectral Graph Neural Network (TMLR 2025) |
| 105 | M2M-GNN | 0.4918
±0.0060 | This paper |
| 137 | FAGCN | 0.4632
±0.0250 best reported | best at pub: Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND (ICLR 2024) best today: Distributed-Order Fractional Graph Operating Network (NeurIPS 2024) Difference within reported uncertainty; not counted as underperformance. |
| 142 | AERO-GNN | 0.4571
±0.0050 | This paper |
| 165 | GGCN | 0.4300
±0.0032 best reported | best at pub: Polynormer: Polynomial-Expressive Graph Transformer in Linear Time (ICLR 2024) |
| 191 | Ord. GNN | 0.3852
±0.0040 | This paper |
| 195 | GOAL | 0.3794
±0.0030 | This paper |
| 198 | DMP | 0.3584
±0.0040 | This paper |
LINKX Benchmarks
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DC-GNN | 0.8669
±0.0022 | |
| 2 | M2M-GNN | 0.8594
±0.0040 | This paper |
| 3 | GloGNN | 0.8574
±0.0042 | |
| 15 | GOAL | 0.8418
±0.0030 | This paper |
| 16 | Ord. GNN | 0.8365
±0.0060 | This paper |
| 20 | GPR-GNN | 0.8354
±0.0032 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) best today: Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach (WWW 2024) |
| 24 | H2GCN | 0.8320
±0.0055 best reported | best at pub: Clarify Confused Nodes via Separated Learning (2023) |
| 26 | ACM-GCN | 0.8298
±0.0063 best reported | best at pub: Clarify Confused Nodes via Separated Learning (2023) Difference within reported uncertainty; not counted as underperformance. |
| 29 | GIN | 0.8268
±0.0032 | |
| 31 | GCN | 0.8247
±0.0020 | This paper |
| 32 | AERO-GNN | 0.8247
±0.0070 | This paper |
| 36 | GAT | 0.8153
±0.0050 | This paper |
| 46 | FAGCN | 0.7697
±0.0069 best reported | best at pub: Clarify Confused Nodes via Separated Learning (2023) |
| 51 | MLP | 0.7534
±0.0064 best reported | best at pub: Clarify Confused Nodes via Separated Learning (2023) |
| 56 | DMP | 0.7385
±0.0070 | This paper |
