Stable Representation Learning via Generalized Learnable Graph Scattering Transform

Shiyu Liu

doi:10.1109/TSP.2026.3660885

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Stable Representation Learning via Generalized Learnable Graph Scattering Transform

2026-02-04

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DOI：10.1109/TSP.2026.3660885

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Abstract

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Graph scattering networks (GSNs) are typically non-trainable graph convolutional networks that realize multi-layer representation learning via analytic graph wavelets with theoretical stability guarantees but are restricted in the flexibility and capacity of representation learning. Recent attempts on trainable GSNs introduce learnable parameters for graph wavelets but are still limited to wavelet families and the modulus nonlinearity. To address this problem, in this paper, we propose the first generalized learnable graph scattering transform (GST) that achieves stable representation learning using a general class of adaptive bandpass graph filters with Lipschitz continuous nonlinearities. The proposed GST learns the bandpass graph filters from arbitrary nonnegative Lipschitz continuous functions, including graph wavelet families and polynomial functions. We demonstrate in theory that learnable graph scattering networks (GSNs) constructed with the proposed GST ensures the upper bounds of difference in learned representations are solely related to the perturbation on graph signal and topology. Furthermore, the proposed GST is generalized to Lipschitz continuous nonlinearites like hyperbolic tangent and ReLU functions beyond the modulus operation with theoretical stability guarantees. Experimental results show that the proposed GSNs evidently outperform existing graph scattering networks in graph and node classification tasks and achieve state-of-the-art performance in node classification by learning multi-scale bandpass representations.

Keywords:

Graph scattering transform

graph representation learning

stability