Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining

A challenge of channel pruning is designing efficient and effective criteria to select channels to prune. A widely used criterion is minimal performance degeneration. To accurately evaluate the truth performance degeneration requires retraining the survived weights to convergence, which is prohibitively slow. Hence existing pruning methods use previous weights (without retraining) to evaluate the performance degeneration. However, we observe the loss changes differ significantly with and without retraining. It motivates us to develop a technique to evaluate true loss changes without retraining, with which channels to prune can be selected more reliably and confidently. We first derive a closed-form estimator of the true loss change per pruning mask change, using influence functions without retraining. Influence function which is from robust statistics reveals the impacts of a training sample on the model's prediction and is repurposed by us to assess impacts on true loss changes. We then show how to assess the importance of all channels simultaneously and develop a novel global channel pruning algorithm accordingly. We conduct extensive experiments to verify the effectiveness of the proposed algorithm. To the best of our knowledge, we are the first that shows evaluating true loss changes for pruning without retraining is possible. This finding will open up opportunities for a series of new paradigms to emerge that differ from existing pruning methods. The code is available at https://github.com/hrcheng1066/IFSO.