Deformable Butterfly: A Highly Structured and Sparse Linear Transform

We introduce a new kind of linear transform named Deformable Butterfly (DeBut) that generalizes the conventional butterfly matrices and can be adapted to various input-output dimensions. It inherits the fine-to-coarse-grained learnable hierarchy of traditional butterflies and when deployed to neural networks, the prominent structures and sparsity in a DeBut layer constitutes a new way for network compression. We apply DeBut as a drop-in replacement of standard fully connected and convolutional layers, and demonstrate its superiority in homogenizing a neural network and rendering it favorable properties such as light weight and low inference complexity, without compromising accuracy. The natural complexity-accuracy tradeoff arising from the myriad deformations of a DeBut layer also opens up new rooms for analytical and practical research. The codes and Appendix are publicly available at: https://github.com/ruilin0212/DeBut.

Exploiting Elasticity in Tensor Ranks for Compressing Neural Networks

Elasticities in depth, width, kernel size and resolution have been explored in compressing deep neural networks (DNNs). Recognizing that the kernels in a convolutional neural network (CNN) are 4-way tensors, we further exploit a new elasticity dimension along the input-output channels. Specifically, a novel nuclear-norm rank minimization factorization (NRMF) approach is proposed to dynamically and globally search for the reduced tensor ranks during training. Correlation between tensor ranks across multiple layers is revealed, and a graceful tradeoff between model size and accuracy is obtained. Experiments then show the superiority of NRMF over the previous non-elastic variational Bayesian matrix factorization (VBMF) scheme.

HOTCAKE: Higher Order Tucker Articulated Kernels for Deeper CNN Compression

The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks (CNNs) by decomposing the 4-way kernel tensor into multi-stage smaller ones. Building on top of Tucker-2 decomposition, we propose a generalized Higher Order Tucker Articulated Kernels (HOTCAKE) scheme comprising four steps: input channel decomposition, guided Tucker rank selection, higher order Tucker decomposition and fine-tuning. By subjecting each CONV layer to HOTCAKE, a highly compressed CNN model with graceful accuracy trade-off is obtained. Experiments show HOTCAKE can compress even pre-compressed models and produce state-of-the-art lightweight networks.