Current unsupervised learning methods depend on end-to-end training via deep learning techniques such as self-supervised learning, with high computational requirements, or employ layer-by-layer training using bio-inspired approaches like Hebbian learning, using local learning rules incompatible with supervised learning. Both approaches are problematic for edge AI hardware that relies on sparse computational resources and would strongly benefit from alternating between unsupervised and supervised learning phases - thus leveraging widely available unlabeled data from the environment as well as labeled training datasets. To solve this challenge, in this work, we introduce a 'self-defined target' that uses Winner-Take-All (WTA) selectivity at the network's final layer, complemented by regularization through biologically inspired homeostasis mechanism. This approach, framework-agnostic and compatible with both global (Backpropagation) and local (Equilibrium propagation) learning rules, achieves a 97.6% test accuracy on the MNIST dataset. Furthermore, we demonstrate that incorporating a hidden layer enhances classification accuracy and the quality of learned features across all training methods, showcasing the advantages of end-to-end unsupervised training. Extending to semi-supervised learning, our method dynamically adjusts the target according to data availability, reaching a 96.6% accuracy with just 600 labeled MNIST samples. This result highlights our 'unsupervised target' strategy's efficacy and flexibility in scenarios ranging from abundant to no labeled data availability.

Analog physical neural networks, which hold promise for improved energy efficiency and speed compared to digital electronic neural networks, are nevertheless typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10). What happens if an analog system is instead operated in an ultra-low-power regime, in which the behavior of the system becomes highly stochastic and the noise is no longer a small perturbation on the signal? In this paper, we study this question in the setting of optical neural networks operated in the limit where some layers use only a single photon to cause a neuron activation. Neuron activations in this limit are dominated by quantum noise from the fundamentally probabilistic nature of single-photon detection of weak optical signals. We show that it is possible to train stochastic optical neural networks to perform deterministic image-classification tasks with high accuracy in spite of the extremely high noise (SNR ~ 1) by using a training procedure that directly models the stochastic behavior of photodetection. We experimentally demonstrated MNIST classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to 0.008 photons per multiply-accumulate (MAC) operation, which is equivalent to 0.003 attojoules of optical energy per MAC. Our experiment used >40x fewer photons per inference than previous state-of-the-art low-optical-energy demonstrations, to achieve the same accuracy of >90%. Our work shows that some extremely stochastic analog systems, including those operating in the limit where quantum noise dominates, can nevertheless be used as layers in neural networks that deterministically perform classification tasks with high accuracy if they are appropriately trained.

Ising machines, which are hardware implementations of the Ising model of coupled spins, have been influential in the development of unsupervised learning algorithms at the origins of Artificial Intelligence (AI). However, their application to AI has been limited due to the complexities in matching supervised training methods with Ising machine physics, even though these methods are essential for achieving high accuracy. In this study, we demonstrate a novel approach to train Ising machines in a supervised way through the Equilibrium Propagation algorithm, achieving comparable results to software-based implementations. We employ the quantum annealing procedure of the D-Wave Ising machine to train a fully-connected neural network on the MNIST dataset. Furthermore, we demonstrate that the machine's connectivity supports convolution operations, enabling the training of a compact convolutional network with minimal spins per neuron. Our findings establish Ising machines as a promising trainable hardware platform for AI, with the potential to enhance machine learning applications.