  While increasingly deep networks are still in general desired for achieving
state-of-the-art performance, for many specific inputs a simpler network might
already suffice. Existing works exploited this observation by learning to skip
convolutional layers in an input-dependent manner. However, we argue their
binary decision scheme, i.e., either fully executing or completely bypassing
one layer for a specific input, can be enhanced by introducing finer-grained,
"softer" decisions. We therefore propose a Dynamic Fractional Skipping (DFS)
framework. The core idea of DFS is to hypothesize layer-wise quantization (to
different bitwidths) as intermediate "soft" choices to be made between fully
utilizing and skipping a layer. For each input, DFS dynamically assigns a
bitwidth to both weights and activations of each layer, where fully executing
and skipping could be viewed as two "extremes" (i.e., full bitwidth and zero
bitwidth). In this way, DFS can "fractionally" exploit a layer's expressive
power during input-adaptive inference, enabling finer-grained
accuracy-computational cost trade-offs. It presents a unified view to link
input-adaptive layer skipping and input-adaptive hybrid quantization. Extensive
experimental results demonstrate the superior tradeoff between computational
cost and model expressive power (accuracy) achieved by DFS. More visualizations
also indicate a smooth and consistent transition in the DFS behaviors,
especially the learned choices between layer skipping and different
quantizations when the total computational budgets vary, validating our
hypothesis that layer quantization could be viewed as intermediate variants of
layer skipping. Our source code and supplementary material are available at
\link{https://github.com/Torment123/DFS}.
