Hessian-Aware Pruning and Optimal Neural Implant

Pruning is an effective method to reduce the memory footprint and FLOPs associated with neural network models. However, existing structured-pruning methods often result in significant accuracy degradation for moderate pruning levels. To address this problem, we introduce a new Hessian Aware Pruning (HAP) method coupled with a Neural Implant approach that uses second-order sensitivity as a metric for structured pruning. The basic idea is to prune insensitive components and to use a Neural Implant for moderately sensitive components, instead of completely pruning them. For the latter approach, the moderately sensitive components are replaced with with a low rank implant that is smaller and less computationally expensive than the original component. We use the relative Hessian trace to measure sensitivity, as opposed to the magnitude based sensitivity metric commonly used in the literature. We test HAP on multiple models on CIFAR-10/ImageNet, and we achieve new state-of-the-art results. Specifically, HAP achieves 94.3\% accuracy ($<0.1\%$ degradation) on PreResNet29 (CIFAR-10), with more than 70\% of parameters pruned. Moreover, for ResNet50 HAP achieves 75.1\% top-1 accuracy (0.5\% degradation) on ImageNet, after pruning more than half of the parameters. The framework has been open sourced and available online.