# Fundamental aspects of noise in analog-hardware neural networks

## TL;DR

This paper analyzes how noise affects the accuracy of analog neural networks, providing insights and strategies for noise management based on theoretical and real-world data.

## Contribution

It offers a comprehensive analysis of noise propagation in analog neural networks, including analytic solutions validated by real-world data, and suggests noise mitigation strategies.

## Key findings

- Analytic solutions match numerical data well.
- Identifies critical components for noise sensitivity.
- Highlights robustness of analog neural networks.

## Abstract

We study and analyze the fundamental aspects of noise propagation in recurrent as well as deep, multi-layer networks. The main focus of our study are neural networks in analogue hardware, yet the methodology provides insight for networks in general. The system under study consists of noisy linear nodes, and we investigate the signal-to-noise ratio at the network's outputs which is the upper limit to such a system's computing accuracy. We consider additive and multiplicative noise which can be purely local as well as correlated across populations of neurons. This covers the chief internal-perturbations of hardware networks and noise amplitudes were obtained from a physically implemented recurrent neural network and therefore correspond to a real-world system. Analytic solutions agree exceptionally well with numerical data, enabling clear identification of the most critical components and aspects for noise management. Focusing on linear nodes isolates the impact of network connections and allows us to derive strategies for mitigating noise. Our work is the starting point in addressing this aspect of analogue neural networks, and our results identify notoriously sensitive points while simultaneously highlighting the robustness of such computational systems.