Pruning Filter in Filter

Pruning has become a very powerful and effective technique to compress and accelerate modern neural networks. Existing pruning methods can be grouped into two categories: filter pruning (FP) and weight pruning (WP). FP wins at hardware compatibility but loses at compression ratio compared with WP. To converge the strength of both methods, we propose to prune the filter in the filter (PFF). Specifically, we treat a filter $F \in \mathbb{R}^{C\times K\times K}$ as $K \times K$ stripes, i.e., $1\times 1$ filters $\in \mathbb{R}^{C}$, then by pruning the stripes instead of the whole filter, PFF achieves finer granularity than traditional FP while being hardware friendly. PFF is implemented by introducing a novel learnable matrix called Filter Skeleton, whose values reflect the optimal shape of each filter. As some rencent work has shown that the pruned architecture is more crucial than the inherited important weights, we argue that the architecture of a single filter, i.e., the Filter Skeleton, also matters. Through extensive experiments, we demonstrate that PFF is more effective compared to the previous FP-based methods and achieves the state-of-art pruning ratio on CIFAR-10 and ImageNet datasets without obvious accuracy drop.