A Gradient Flow Framework For Analyzing Network Pruning
This provides theoretical insights for researchers in neural network compression, though it is incremental as it builds on existing pruning methods.
The paper tackled the problem of explaining why early pruning methods work well by developing a gradient flow framework that unifies importance measures, showing that magnitude-based pruning leads to faster convergence, loss-preservation methods maintain dynamics, and gradient-norm pruning can harm performance, with validation on models like VGG-13 and ResNet-56 on CIFAR datasets.
Recent network pruning methods focus on pruning models early-on in training. To estimate the impact of removing a parameter, these methods use importance measures that were originally designed to prune trained models. Despite lacking justification for their use early-on in training, such measures result in surprisingly low accuracy loss. To better explain this behavior, we develop a general framework that uses gradient flow to unify state-of-the-art importance measures through the norm of model parameters. We use this framework to determine the relationship between pruning measures and evolution of model parameters, establishing several results related to pruning models early-on in training: (i) magnitude-based pruning removes parameters that contribute least to reduction in loss, resulting in models that converge faster than magnitude-agnostic methods; (ii) loss-preservation based pruning preserves first-order model evolution dynamics and is therefore appropriate for pruning minimally trained models; and (iii) gradient-norm based pruning affects second-order model evolution dynamics, such that increasing gradient norm via pruning can produce poorly performing models. We validate our claims on several VGG-13, MobileNet-V1, and ResNet-56 models trained on CIFAR-10/CIFAR-100. Code available at https://github.com/EkdeepSLubana/flowandprune.