Optimal Pruning for Neural Architectures using Fisher Information Distances

2026-09-14

AI Summary

该研究提出了一种基于Fisher信息距离的神经网络参数剪枝方案，通过计算模型空间中的测地线距离来确定最优剪枝策略，提高了模型在MNIST和CIFAR-10数据集上的准确性和效率。

Abstract

A new scheme for parameter pruning is introduced, derived from the differential-geometric distance in model space. Pruning a parameter sets its value to zero, representing a displacement of the model to the hypersurface on which that parameter vanishes. The minimal distance from the unpruned model to this hypersurface is naturally computed via the geodesic distance in the model space as determined by the Fisher information metric. This distance determines the true change in the model, and its performance, under pruning. By analysing progressively more faithful approximations of this geodesic distance a natural hierarchy of optimality for pruning methods is determined. This starts with the traditional magnitude pruning, then develops into new more sophisticated and effective pruning schemes. The method is demonstrated for both fully-connected networks and vision transformers, on MNIST and CIFAR-10, over the complete $0$-$100\%$ pruning range and across five random seeds. It outperforms pruning by parameter magnitude and by the local Fisher information alone in every architecture and dataset combination considered, on both accuracy and the Matthews correlation coefficient. Additionally, analysis of different levels of geodesic approximation produces intermediate pruning schemes that are computationally efficient and maintain near-optimal performance. This geometric picture supplies not only a state-of-the-art pruning methodology for AI models, but also a verified and mathematically-motivated justification for pruning schemes.

Problem

• Neural Network Pruning
• Fisher Information
• Geodesic Distance
• Model Optimization

Innovation

• Fisher Information Distances
• Geodesic Distance
• Parameter Pruning
• Model Space
• Neural Architectures