# Speeding-Up Back-Propagation in DNN: Approximate Outer Product with Memory

arXiv: https://arxiv.org/abs/2110.09164 · HTML: https://mlsanity.com/paper/2110.09164/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Gradient Sparsification for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1710.09854/) (2017)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Understanding Top-k Sparsification in Distributed Deep Learning](https://mlsanity.com/paper/1911.08772/) (2019)
- [VR-SGD: A Simple Stochastic Variance Reduction Method for Machine Learning](https://mlsanity.com/paper/1802.09932/) (2018)

## Built on by (most cited first, 1 of 1)

- [Gradient Correction beyond Gradient Descent](https://mlsanity.com/paper/2203.08345/) (2022)

## Abstract (arXiv)

In this paper, an algorithm for approximate evaluation of back-propagation in DNN training is considered, which we term Approximate Outer Product Gradient Descent with Memory (Mem-AOP-GD). The Mem-AOP-GD algorithm implements an approximation of the stochastic gradient descent by considering only a subset of the outer products involved in the matrix multiplications that encompass backpropagation. In order to correct for the inherent bias in this approximation, the algorithm retains in memory an accumulation of the outer products that are not used in the approximation. We investigate the performance of the proposed algorithm in terms of DNN training loss under two design parameters: (i) the number of outer products used for the approximation, and (ii) the policy used to select such outer products. We experimentally show that significant improvements in computational complexity as well as accuracy can indeed be obtained through Mem-AOPGD.