An Efficient Polynomial Multiplication Derived Implementation of Convolution in Neural Networks

Abstract

Convolution is the most time consuming computation kernel in Convolutional Neural Network (CNN) applications and the majority of Graph Neural Network (GNN) applications. To achieve good convolution performance, current NN libraries such as cuDNN usually transform the naive convolution problem into either the matrix vector multiplication form, called the im2col+MM approach, or into the Fourier domain representation, namely the FFT approach. Both approaches either introduce significant amount of data redundancy to reduce the number of data passes and to leverage highly tuned linear algebra libraries, or avoid data redundancy but require multiple passes on input. Therefore, no implementation of convolution can outperform others in all cases. In this paper, we introduce a novel transformation that reinterprete the convolution in NN as a polynomial multiplication problem. By carefully constructing a number of conceptual polynomials, NN’s convolution essentially becomes a well-known problem of calculating the coefficients in the product of two polynomials. We evaluate our approach in multiple ways: at the API level comparing it with one of the most widely used NN libraries cuDNN, as well as implementing it in PyTorch and comparing the performance with benchmark networks. On three NVIDIA GPUs 3090Ti, V100 and A10G, our approach outperforms cuDNN over a broad range of parameters with the max speedups of 34.6%, 43.1% and 33.6% on these GPUs, respectively.