Physical neural networks (PNNs) are a class of neural-like networks that leverage the properties of physical systems to perform computation. While PNNs are so far a niche research area with small-scale laboratory demonstrations, they are arguably one of the most underappreciated important opportunities in modern AI. Could we train AI models 1000x larger than current ones? Could we do this and also have them perform inference locally and privately on edge devices, such as smartphones or sensors? Research over the past few years has shown that the answer to all these questions is likely "yes, with enough research": PNNs could one day radically change what is possible and practical for AI systems. To do this will however require rethinking both how AI models work, and how they are trained - primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs at large scale, many methods including backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs, and so far no method has been shown to scale to the same scale and performance as the backpropagation algorithm widely used in deep learning today. However, this is rapidly changing, and a diverse ecosystem of training techniques provides clues for how PNNs may one day be utilized to create both more efficient realizations of current-scale AI models, and to enable unprecedented-scale models.

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase unceasingly. This growth of the deep learning models is accompanied by issues related to their considerable energy consumption, both during the training and inference phases, as well as their scalability. Although a number of work based on unconventional physical systems have been proposed which addresses the issue of energy efficiency in the inference phase, efficient training of deep learning models has remained unaddressed. So far, training of digital deep learning models mainly relies on backpropagation, which is not suitable for physical implementation as it requires perfect knowledge of the computation performed in the so-called forward pass of the neural network. Here, we tackle this issue by proposing a simple deep neural network architecture augmented by a biologically plausible learning algorithm, referred to as "model-free forward-forward training". The proposed architecture enables training deep physical neural networks consisting of layers of physical nonlinear systems, without requiring detailed knowledge of the nonlinear physical layers' properties. We show that our method outperforms state-of-the-art hardware-aware training methods by improving training speed, decreasing digital computations, and reducing power consumption in physical systems. We demonstrate the adaptability of the proposed method, even in systems exposed to dynamic or unpredictable external perturbations. To showcase the universality of our approach, we train diverse wave-based physical neural networks that vary in the underlying wave phenomenon and the type of non-linearity they use, to perform vowel and image classification tasks experimentally.