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Title: Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.  more » « less
Award ID(s):
1845856
NSF-PAR ID:
10269836
Author(s) / Creator(s):
; ; ;
Editor(s):
Lu, Jianfeng; Ward, Rachel
Date Published:
Journal Name:
Proceedings of Machine Learning Research
Volume:
107
ISSN:
2640-3498
Page Range / eLocation ID:
570-604
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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