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. 2024:72:2939-2952.
doi: 10.1109/tsp.2024.3378001. Epub 2024 Mar 18.

Learnable Filters for Geometric Scattering Modules

Alexander Tong  1   2 , Frederik Wenkel  3   2 , Dhananjay Bhaskar  4 , Kincaid Macdonald  5 , Jackson Grady  6 , Michael Perlmutter  5 , Smita Krishnaswamy  7 , Guy Wolf  3   2
Affiliations

Learnable Filters for Geometric Scattering Modules

Alexander Tong et al. IEEE Trans Signal Process. 2024.

Abstract

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks. Our results show that LEGS-based networks match or outperforms popular GNNs, as well as the original geometric scattering construction, on many datasets, in particular in biochemical domains, while retaining certain mathematical properties of handcrafted (non-learned) geometric scattering.

Keywords: Geometric Scattering; Graph Neural Networks; Graph Signal Processing.

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Figures

Fig. 4.
Fig. 4.
Two graphs with similar structure consisting of an 8-cycle. Each cycle has two nodes that are connected to another node, which (with respected to shortest-path distance) are 3 steps (a) and 4 steps (b) apart, respectively.
Fig. 1.
Fig. 1.
LEGS module learns to select the appropriate scattering scales from the data.
Fig. 2.
Fig. 2.
Enzyme class exchange preferences empirically observed in [32], and estimated from LEGS and GCN embeddings.
Fig. 3.
Fig. 3.
CASP dataset LEGS-FCN % decrease over GCN in MSE of GDT prediction vs. Average GDT score.
See this image and copyright information in PMC

References

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