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arXiv · 2503.19215

On Symmetries in Convolutional Weights

Bilal Alsallakh·Timothy Wroge·Vivek Miglani·Narine Kokhlikyan
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Abstract

We explore the symmetry of the mean k x k weight kernel in each layer of various convolutional neural networks. Unlike individual neurons, the mean kernels in internal layers tend to be symmetric about their centers instead of favoring specific directions. We investigate why this symmetry emerges in various datasets and models, and how it is impacted by certain architectural choices. We show how symmetry correlates with desirable properties such as shift and flip consistency, and might constitute an inherent inductive bias in convolutional neural networks.

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Bilal Alsallakh, Timothy Wroge, Vivek Miglani, Narine Kokhlikyan. 2025-03-24. On Symmetries in Convolutional Weights. https://arxiv.org/abs/2503.19215

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