# Training deep neural networks with low precision multiplications

arXiv: https://arxiv.org/abs/1412.7024 · HTML: https://mlsanity.com/paper/1412.7024/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2014.

## Built on by (most cited first, 5 of 5)

- [Semantic Segmentation using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2209.08667/) (2022)
- [Soft Threshold Ternary Networks](https://mlsanity.com/paper/2204.01234/) (2022)
- [Analyzing Compression Techniques for Computer Vision](https://mlsanity.com/paper/2305.08075/) (2023)
- [Ego-METAS: Egocentric online Multimodal Energy-efficient Temporal Action Segmentation benchmark](https://mlsanity.com/paper/2606.02246/) (2026)
- [AS-FedBridge: Pseudo-Spike Bridge Distillation for Heterogeneous ANN-SNN Federated Learning](https://mlsanity.com/paper/2608.03324/) (2026)

## Abstract (arXiv)

Multipliers are the most space and power-hungry arithmetic operators of the digital implementation of deep neural networks. We train a set of state-of-the-art neural networks (Maxout networks) on three benchmark datasets: MNIST, CIFAR-10 and SVHN. They are trained with three distinct formats: floating point, fixed point and dynamic fixed point. For each of those datasets and for each of those formats, we assess the impact of the precision of the multiplications on the final error after training. We find that very low precision is sufficient not just for running trained networks but also for training them. For example, it is possible to train Maxout networks with 10 bits multiplications.