# Sparse Deep Neural Network Exact Solutions

arXiv: https://arxiv.org/abs/1807.03165 · HTML: https://mlsanity.com/paper/1807.03165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2018.

## Built on by (most cited first, 2 of 2)

- [Truly Sparse Neural Networks at Scale](https://mlsanity.com/paper/2102.01732/) (2021)
- [Exploring the Impact of Serverless Computing on Peer To Peer Training Machine Learning](https://mlsanity.com/paper/2309.14139/) (2023)

## Abstract (arXiv)

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by operations on the weight matrices describing the DNN. As DNNs incorporate more layers and more neurons per layers, these weight matrices may be required to be sparse because of memory limitations. Sparse DNNs are one possible approach, but the underlying theory is in the early stages of development and presents a number of challenges, including determining the accuracy of inference and selecting nonzero weights for training. Associative array algebra has been developed by the big data community to combine and extend database, matrix, and graph/network concepts for use in large, sparse data problems. Applying this mathematics to DNNs simplifies the formulation of DNN mathematics and reveals that DNNs are linear over oscillating semirings. This work uses associative array DNNs to construct exact solutions and corresponding perturbation models to the rectified linear unit (ReLU) DNN equations that can be used to construct test vectors for sparse DNN implementations over various precisions. These solutions can be used for DNN verification, theoretical explorations of DNN properties, and a starting point for the challenge of sparse training.