Change-of-Basis Pruning via Rotational Invariance

TL;DR

This paper introduces a rotationally invariant neural network design with two-subspace radial activations to facilitate change-of-basis pruning, achieving high parameter reduction with minimal accuracy loss.

Contribution

The work proposes TSRAs, a novel activation family invariant to orthogonal transformations, enabling effective change-of-basis pruning without extra parameters.

Findings

CoB+TSRA improves pruning efficiency across ratios

Achieves 90-96% parameter pruning with minimal accuracy loss

Extends reliable pruning frontier from 30% to 70%

Abstract

Structured pruning removes entire neurons or channels, but its effectiveness depends on how importance is distributed across the representation space. Change-of-basis (CoB) pruning addresses this challenge by applying orthogonal linear transformations that concentrate importance within certain dimensions. However, many standard deep learning architectures are not inherently invariant to such transformations. To enable compatibility, we introduce two-subspace radial activations (TSRAs): an activation family that is invariant to orthogonal linear transformations applied independently within its two activation subspaces. This invariance allows CoB transformations to be merged into surrounding weights without incurring extra parameters. We position this work as a proof-of-concept that a rotationally invariant design may offer a principled approach towards change-of-basis pruning. We do not provide an analysis of multiple TSRA candidates nor do we explore weight initialization for any TSRAs. These limitations, combined with other necessary modifications we make to permit rotational invariance, result in a slight accuracy drop of $4.52\%$ compared to a ReLU-based control. However, using activation-magnitude importance, VGG-16 implementing our CoB+TSRA framework shows encouraging results on CIFAR-10. Under fixed-ratio structured pruning, CoB improves accuracy over a TSRA baseline at all pruning ratios and extends reliable pruning frontier from roughly $30\%$ to $70\%$ of parameters without post-prune fine tuning. Under threshold-based pruning strategies, CoB prunes $90-96\%$ of parameters while maintaining $1-6\%$ accuracy drop after fine-tuning. Together, these results indicate that rotationally invariant architectures may offer a promising path towards CoB pruning.