The Indirect Convolution Algorithm

TL;DR

The paper introduces the Indirect Convolution algorithm, which improves efficiency over traditional GEMM-based convolution methods by eliminating the need for data reshuffling, thus reducing memory overhead and enhancing performance for various convolution configurations.

Contribution

The Indirect Convolution algorithm offers a novel approach that avoids data reshaping, broadening application scope and outperforming GEMM-based methods in many scenarios.

Findings

Reduces memory overhead proportionally to input channels.

Outperforms GEMM-based algorithms by up to 62% on certain parameters.

Minor performance reduction on 1x1 stride-1 convolutions.

Abstract

Deep learning frameworks commonly implement convolution operators with GEMM-based algorithms. In these algorithms, convolution is implemented on top of matrix-matrix multiplication (GEMM) functions, provided by highly optimized BLAS libraries. Convolutions with 1x1 kernels can be directly represented as a GEMM call, but convolutions with larger kernels require a special memory layout transformation - im2col or im2row - to fit into GEMM interface. The Indirect Convolution algorithm provides the efficiency of the GEMM primitive without the overhead of im2col transformation. In contrast to GEMM-based algorithms, the Indirect Convolution does not reshuffle the data to fit into the GEMM primitive but introduces an indirection buffer - a buffer of pointers to the start of each row of image pixels. This broadens the application of our modified GEMM function to convolutions with arbitrary kernel size, padding, stride, and dilation. The Indirect Convolution algorithm reduces memory overhead proportionally to the number of input channels and outperforms the GEMM-based algorithm by up to 62% on convolution parameters which involve im2col transformations in GEMM-based algorithms. This, however, comes at cost of minor performance reduction on 1x1 stride-1 convolutions.