# Fast 2D Convolutions and Cross-Correlations Using Scalable Architectures

arXiv: https://arxiv.org/abs/2112.13150 · HTML: https://mlsanity.com/paper/2112.13150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 33 references that are in the map.
- First posted on arXiv 24 Dec 2021.

## Builds on (most cited first, 1 of 1)

- [Precision-Energy-Throughput Scaling Of Generic Matrix Multiplication and Convolution Kernels Via Linear Projections](https://mlsanity.com/paper/1411.2860/) (2014)

## Abstract (arXiv)

The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and cross-correlations in the transform domain. This is accomplished through the use of the Discrete Periodic Radon Transform (DPRT) for general kernels and the use of SVD-LU decompositions for low-rank kernels. The approach uses scalable architectures that can be fitted into modern FPGA and Zynq-SOC devices. Based on different types of available resources, for P× P blocks, 2D convolutions and cross-correlations can be computed in just O(P) clock cycles up to O(P2) clock cycles. Thus, there is a trade-off between performance and required numbers and types of resources. We provide implementations of the proposed architectures using modern programmable devices (Virtex-7 and Zynq-SOC). Based on the amounts and types of required resources, we show that the proposed approaches significantly outperform current methods.