# Optical neural networks with intensity‑based projection layers as effective nonlinear activations

## TL;DR

This paper introduces a new method for optical neural networks using intensity-based projection layers as nonlinear activations, improving efficiency and performance.

## Contribution

The novel use of optical intensity measurements as nonlinear activation functions in optical neural networks.

## Key findings

- Projection layers effectively replace traditional nonlinear activations in various tasks like image classification and reconstruction.
- The method performs robustly under noisy conditions and supports quaternion-valued representations for multi-dimensional features.
- The approach is demonstrated in a β-VAE framework for learning interpretable physical parameters.

## Abstract

Optical neural networks (ONNs) offer significant advantages in speed and energy efficiency by exploiting the parallelism of light. A key challenge in their design is the implementation of nonlinear activation functions using physically realizable operations. In this work, we propose the use of optical intensity measurements—as projections from complex or quaternion-valued fields to real-valued magnitudes together with amplitude or phase encoding to next layer—as effective alternatives to traditional nonlinear activation functions in neural networks. Through systematic evaluations across image classification, image reconstruction, and physical parameter inference, we validate the effectiveness and robustness of projection layers as nonlinear activation mechanisms. The approach extends naturally to quaternion-valued representations, capturing multi-dimensional features such as amplitude, phase, and polarization. We further assess performance under noisy conditions and demonstrate its utility in a β-VAE framework for learning interpretable physical parameters. This projection-based approach not only leverages the advantages of optical computing but also establishes a scalable and hardware-efficient foundation for deep ONNs with broad applicability in image recognition, signal processing, and scientific inference.

The online version contains supplementary material available at 10.1038/s41598-025-30632-y.