# Winograd Convolution for DNNs: Beyond linear polynomials

arXiv: https://arxiv.org/abs/1905.05233 · HTML: https://mlsanity.com/paper/1905.05233/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2019.

## Built on by (most cited first, 4 of 4)

- [Winograd Convolution for Deep Neural Networks: Efficient Point Selection](https://mlsanity.com/paper/2201.10369/) (2022)
- [Going Further With Winograd Convolutions: Tap-Wise Quantization for Efficient Inference on 4x4 Tile](https://mlsanity.com/paper/2209.12982/) (2022)
- [SFC: Achieve Accurate Fast Convolution under Low-precision Arithmetic](https://mlsanity.com/paper/2407.02913/) (2024)
- [Fast Convolution based on Winograd Minimum Filtering: Introduction and Development](https://mlsanity.com/paper/2111.00977/) (2021)

## Abstract (arXiv)

Winograd convolution is widely used in deep neural networks (DNNs). Existing work for DNNs considers only the subset Winograd algorithms that are equivalent to Toom-Cook convolution. We investigate a wider range of Winograd algorithms for DNNs and show that these additional algorithms can significantly improve floating point (FP) accuracy in many cases. We present results for three FP formats: fp32, fp16 and bf16 (a truncated form of fp32) using 2000 inputs from the ImageNet dataset. We found that in fp16 this approach gives us up to 6.5 times better image recognition accuracy in one important case while maintaining the same number of elementwise multiplication operations in the innermost loop. In bf16 the convolution can be computed using 5% fewer innermost loop multiplications than with currently used Winograd algorithms while keeping the accuracy of image recognition the same as for direct convolution method.