# Gradient descent in materia through homodyne gradient extraction

## TL;DR

This paper introduces a new method for efficient gradient descent in physical systems using homodyne detection, reducing energy consumption in deep learning.

## Contribution

The novel contribution is a scalable gradient-extraction method using homodyne detection for material-based learning systems.

## Key findings

- Homodyne gradient extraction enables gradient descent directly in physical systems without analytical descriptions.
- The method uses sinusoidal perturbations at distinct frequencies to robustly obtain gradient information.
- It is demonstrated in reconfigurable nonlinear-processing units and shown to be broadly applicable.

## Abstract

Deep learning, a multilayered neural-network approach inspired by the brain, has revolutionized machine learning. Its success relies on backpropagation, which computes gradients of a loss function for use in gradient descent. However, digital implementations are energy hungry, with power demands limiting many applications. This has motivated specialized hardware, from neuromorphic CMOS and photonic tensor cores to unconventional material-based systems. Learning in such systems, for example via artificial evolution, equilibrium propagation, or surrogate modelling, is typically complicated and slow. Here, we demonstrate a simple gradient-extraction method based on homodyne detection, enabling gradient descent directly in physical systems without the need for an analytical description. By perturbing parameters with sinusoidal waveforms at distinct frequencies, we robustly obtain gradient information in a scalable manner. We illustrate the method in reconfigurable nonlinear-processing units and argue for broad applicability. Homodyne gradient extraction can in principle be fully implemented in materia, facilitating autonomously learning material systems.

Training deep neural networks by backpropagation consumes significant energy in digital hardware. Boon and Cassola et al. show that homodyne detection can be used to extract gradients directly in a physical device, enabling efficient gradient descent and offering a scalable route to material-based learning.