Graph Scattering beyond Wavelet Shackles
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Abstract (arXiv)
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-set non-preserving case is treated by utilizing recently developed mathematical-physics based tools. Energy propagation through the network layers is investigated and related to truncation stability. New methods of graph-level feature aggregation are introduced and stability of the resulting composite scattering architectures is established. Finally, scattering transforms are extended to edge- and higher order tensorial input. Theoretical results are complemented by numerical investigations: Suitably chosen cattering networks conforming to the developed theory perform better than traditional graph-wavelet based scattering approaches in social network graph classification tasks and significantly outperform other graph-based learning approaches to regression of quantum-chemical energies on QM7.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 27 of its 55 references that are in the map. First posted on arXiv 26 Jan 2023.
Builds on
27 of 55 references.
References · 27
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15 more
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Citing papers per year: 2023: 1; 2024: 1.
2 papers.