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.

翻译：本文聚焦于三维卷积神经网络中的Winograd变换，相较于二维版本，三维卷积网络存在更严重的过参数化问题。Winograd参数的过度增长不仅加剧了训练复杂度，更由于Winograd域中逐元素乘积的规模庞大，阻碍了实际加速效果。我们尝试通过引入低秩Winograd变换来减少可训练参数，这是一种新颖的训练范式，将原始大张量分解为两个存储需求更小的可训练张量，从而显著降低复杂度。基于低秩Winograd变换，我们进一步提出面向低秩的稀疏粒度方法，用于衡量列间参数重要性。通过仅在逐元素乘积中保留非零列，该稀疏粒度方法能够生成高度规则的稀疏模式，从而获得有效的Winograd加速。为深入验证方法有效性，我们在三维卷积网络上进行了大量实验。结果表明，我们的低秩Winograd变换显著优于传统Winograd变换。此外，相较于传统方法，我们提出的面向低秩的稀疏粒度方法可实现实际的Winograd加速。