Encoding Involutory Invariance in Neural Networks

• URL: http://arxiv.org/abs/2106.12891v1
• Date: Mon, 7 Jun 2021 16:07:15 GMT
• Title: Encoding Involutory Invariance in Neural Networks
• Authors: Anwesh Bhattacharya, Marios Mattheakis, Pavlos Protopapas
• Abstract summary: In certain situations, Neural Networks (NN) are trained upon data that obey underlying physical symmetries. In this work, we explore a special kind of symmetry where functions are invariant with respect to involutory linear/affine transformations up to parity. Numerical experiments indicate that the proposed models outperform baseline networks while respecting the imposed symmetry. An adaption of our technique to convolutional NN classification tasks for datasets with inherent horizontal/vertical reflection symmetry has also been proposed.
• Score: 1.6371837018687636
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In certain situations, Neural Networks (NN) are trained upon data that obey underlying physical symmetries. However, it is not guaranteed that NNs will obey the underlying symmetry unless embedded in the network structure. In this work, we explore a special kind of symmetry where functions are invariant with respect to involutory linear/affine transformations up to parity $p=\pm 1$. We develop mathematical theorems and propose NN architectures that ensure invariance and universal approximation properties. Numerical experiments indicate that the proposed models outperform baseline networks while respecting the imposed symmetry. An adaption of our technique to convolutional NN classification tasks for datasets with inherent horizontal/vertical reflection symmetry has also been proposed.

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