# Learning may need only a few bits of synaptic precision

arXiv: https://arxiv.org/abs/1602.04129 · HTML: https://mlsanity.com/paper/1602.04129/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2016.

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

- [Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape](https://mlsanity.com/paper/2201.08025/) (2022)
- [Deep learning via message passing algorithms based on belief propagation](https://mlsanity.com/paper/2110.14583/) (2021)
- [High-dimensional learning of narrow neural networks](https://mlsanity.com/paper/2409.13904/) (2024)
- [High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator](https://mlsanity.com/paper/2510.10693/) (2025)
- [Effect of Weight Quantization on Learning Models by Typical Case Analysis](https://mlsanity.com/paper/2401.17269/) (2024)

## Abstract (arXiv)

Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware implementation considerations as well. In this paper we extend a previous large deviations analysis which unveiled the existence of peculiar dense regions in the space of synaptic states which accounts for the possibility of learning efficiently in networks with binary synapses. We extend the analysis to synapses with multiple states and generally more plausible biological features. The results clearly indicate that the overall qualitative picture is unchanged with respect to the binary case, and very robust to variation of the details of the model. We also provide quantitative results which suggest that the advantages of increasing the synaptic precision (i.e.~the number of internal synaptic states) rapidly vanish after the first few bits, and therefore that, for practical applications, only few bits may be needed for near-optimal performance, consistently with recent biological findings. Finally, we demonstrate how the theoretical analysis can be exploited to design efficient algorithmic search strategies.