An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architectures

TL;DR

This paper introduces AOC, an adaptive orthogonal convolution scheme that enhances the scalability and efficiency of orthogonal CNN layers, enabling more practical large-scale applications and architectures.

Contribution

We propose AOC, a scalable method extending BCOP, allowing efficient construction of orthogonal convolutions with modern features, and provide an open-source implementation.

Findings

AOC produces expressive, scalable models.

The method improves efficiency in large-scale applications.

Open-source package Orthogonium is available.

Abstract

Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable gradient propagation makes them valuable for a large range of problems. Despite their promise, the deployment of orthogonal convolution in large-scale applications is a significant challenge due to computational overhead and limited support for modern features like strides, dilations, group convolutions, and transposed convolutions. In this paper, we introduce AOC (Adaptative Orthogonal Convolution), a scalable method that extends a previous method (BCOP), effectively overcoming existing limitations in the construction of orthogonal convolutions. This advancement unlocks the construction of architectures that were previously considered impractical. We demonstrate through our experiments that our method produces expressive models that become increasingly efficient as they scale. To foster further advancement, we provide an open-source python package implementing this method, called Orthogonium ( https://github.com/deel-ai/orthogonium ) .