Bio-inspired backpropagation-free training for optical neural networks.

Optical Neural Networks (ONNs) can perform matrix operations at the speed of light and are expected to bring revolutionary advances in energy-efficient computing. However, traditional ONNs (T-ONNs) rely heavily on error backpropagation algorithms, which are fundamentally incompatible with physical optical systems due to the lack of reciprocal error paths and extreme sensitivity to fabrication imperfections. In this paper, we propose a bio-inspired backpropagation-free optical neural network (B-ONN) that circumvents gradient backpropagation through a layer-wise target propagation mechanism. By introducing trainable error convolution kernels, each layer can perform local learning based on target signals rather than chain-ruled gradients, eliminating the need for precise optical conjugation between forward and backward paths. Experimental results demonstrate that B-ONN achieves comparable accuracy to T-ONN on both the MNIST and Fashion-MNIST datasets, with 93.25% and 82.28% accuracy, respectively. Moreover, B-ONN demonstrates superior robustness against phase noise (75% accuracy at σ ≈ 0.4π) and alignment errors (75% accuracy within ±3 pixels). We physically validated B-ONN using a programmable spatial light modulator (SLM) system, achieving 95% accuracy in handwritten digit recognition. Furthermore, we successfully implemented chip-scale integration via nano printing, maintaining 94% accuracy, confirming B-ONN's effective transferability from programmable setups to fixed devices. Crucially, B-ONN learns smooth phase distributions that provide inherent structural robustness without requiring noise-augmented training. Its local learning rules also support asynchronous parallel updates in scalable deep architectures. This work opens a practical and feasible path for deploying optical computing systems in real-world applications.