  This paper focuses on Winograd transformation in 3D convolutional neural
networks (CNNs) that are more over-parameterized compared with the 2D version.
The over-increasing Winograd parameters not only exacerbate training complexity
but also barricade the practical speedups due simply to the volume of
element-wise products in the Winograd domain. We attempt to reduce trainable
parameters by introducing a low-rank Winograd transformation, a novel training
paradigm that decouples the original large tensor into two less
storage-required trainable tensors, leading to a significant complexity
reduction. Built upon our low-rank Winograd transformation, we take one step
ahead by proposing a low-rank oriented sparse granularity that measures
column-wise parameter importance. By simply involving the non-zero columns in
the element-wise product, our sparse granularity is empowered with the ability
to produce a very regular sparse pattern to acquire effectual Winograd
speedups. To better understand the efficacy of our method, we perform extensive
experiments on 3D CNNs. Results manifest that our low-rank Winograd
transformation well outperforms the vanilla Winograd transformation. We also
show that our proposed low-rank oriented sparse granularity permits practical
Winograd acceleration compared with the vanilla counterpart.
