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arXiv · 2210.04345

LieGG: Studying Learned Lie Group Generators

Artem Moskalev·Anna Sepliarskaia·Ivan Sosnovik·Arnold Smeulders
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Abstract

Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is advantageous for robust networks to learn symmetries directly from the data to fit a task function. In this paper, we present a method to extract symmetries learned by a neural network and to evaluate the degree to which a network is invariant to them. With our method, we are able to explicitly retrieve learned invariances in a form of the generators of corresponding Lie-groups without prior knowledge of symmetries in the data. We use the proposed method to study how symmetrical properties depend on a neural network's parameterization and configuration. We found that the ability of a network to learn symmetries generalizes over a range of architectures. However, the quality of learned symmetries depends on the depth and the number of parameters.

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Artem Moskalev, Anna Sepliarskaia, Ivan Sosnovik, Arnold Smeulders. 2022-10-09. LieGG: Studying Learned Lie Group Generators. https://arxiv.org/abs/2210.04345

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