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arXiv · 2311.02922

Truly Scale-Equivariant Deep Nets with Fourier Layers

Md Ashiqur Rahman·Raymond A. Yeh
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Abstract

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

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Md Ashiqur Rahman, Raymond A. Yeh. 2023-11-06. Truly Scale-Equivariant Deep Nets with Fourier Layers. https://arxiv.org/abs/2311.02922

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