# The Indirect Convolution Algorithm

arXiv: https://arxiv.org/abs/1907.02129 · HTML: https://mlsanity.com/paper/1907.02129/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2019.

## Built on by (most cited first, 7 of 7)

- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [Accelerating Deep Neural Networks via Semi-Structured Activation Sparsity](https://mlsanity.com/paper/2309.06626/) (2023)
- [A New Frontier of AI: On-Device AI Training and Personalization](https://mlsanity.com/paper/2206.04688/) (2022)
- [TCN Mapping Optimization for Ultra-Low Power Time-Series Edge Inference](https://mlsanity.com/paper/2203.12925/) (2022)
- [Advancing Direct Convolution using Convolution Slicing Optimization and ISA Extensions](https://mlsanity.com/paper/2303.04739/) (2023)
- [Kernel-Segregated Transpose Convolution Operation](https://mlsanity.com/paper/2209.03704/) (2022)
- [Threshold Neuron: A Brain-inspired Artificial Neuron for Efficient On-device Inference](https://mlsanity.com/paper/2412.13902/) (2024)

## Abstract (arXiv)

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.