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Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching
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Proposes Adaptive Message Passing (AMP), a variational framework that lets deep graph networks learn their depth and softly filter messages per layer, improving long-range performance on synthetic and LRGB chemical graph benchmarks.
Problem
Message passing graph networks fail to capture long-range dependencies due to oversmoothing, oversquashing, and underreaching, and depth is typically tuned by costly grid search.
Approach
Extends unbounded depth networks to graphs with a variational ELBO over a learned depth distribution (truncated Poisson/folded-normal families) plus a differentiable soft message filter per node and layer, and a layer-wise readout, so the model learns how many layers to use and which messages to send.
Key results
- On synthetic tasks AMP reduces log10 MSE vs base models on average by 63% (Diameter), 72% (SSSP), and 32% (Eccentricity).
- On peptides-func AMP improves AP by roughly 2 to 3.4% over base models (AMP-GCN 0.7161 AP vs GCN 0.6860 re-evaluated).
- On peptides-struct AMP-GCN reaches 0.2446 MAE, placing AMP at state-of-the-art levels considering standard deviation overlap.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn adaptive depth and filter messages rather than use fixed synchronous message passing | Message-passing architectures · Diameter | log10(MSE): -63% average relative improvement | Helped |
| Learn adaptive depth and filter messages rather than use fixed synchronous message passing | Message-passing architectures · SSSP | log10(MSE): -72% average relative improvement | Helped |
| Learn adaptive depth and filter messages rather than use fixed synchronous message passing | Message-passing architectures · Eccentricity | log10(MSE): -32% average relative improvement | Helped |
| Add adaptive depth and message filtering | GCN, GINE, and GatedGCN · peptides-func | Test AP: 2 to 3.4 % | Helped |
| Add adaptive depth and message filtering | GCN, GINE, and GatedGCN · peptides-struct | Test MAE | Helped |
| Add input-based or embedding-based message filtering instead of no filtering (ablation) | AMP_GCN · Evaluated datasets | task score | Helped |
Surprising findings
- Learned depth on Diameter is about 20 layers, far deeper than the usual 10-layer setups in prior LRGB work.
- Filtering messages can reduce sensitivity yet improve performance, challenging the view that higher sensitivity mitigates oversquashing.
Limitations
- Per-layer readouts add parameter and compute overhead that grows with depth.
- Choice of distribution family and filtering strategy (input vs embedding) is a hyper-parameter that must be selected empirically.
- Re-evaluated baselines and reported gains on peptides-struct overlap within standard deviations.
Experimental setup
Datasets: Diameter SSSP Eccentricity peptides-func peptides-struct
Benchmarks: Diameter SSSP Eccentricity peptides-func peptides-struct
Metrics: log10 MSE average precision mean absolute error
Baselines: GCN GAT GraphSAGE GIN GCNII DGC GRAND ADGN GINE GatedGCN GPS GRIT
Builds on: unbounded depth networks GCN GIN ADGN
Closest papers by meaning
- Learning Long Range Dependencies on Graphs via Random Walks (ICLR 2025 · similarity 0.87)
- On Measuring Long-Range Interactions in Graph Neural Networks (ICML 2025 · similarity 0.87)
- Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models (NeurIPS 2025 · similarity 0.87)
- Long Range Propagation on Continuous-Time Dynamic Graphs (ICML 2024 · similarity 0.86)
- On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems (AAAI 2025 · similarity 0.86)
- Towards Dynamic Message Passing on Graphs (NeurIPS 2024 · similarity 0.86)
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