Physical Deep Learning Based on Optimal Control of Dynamical Systems

Deep learning is the backbone of artificial-intelligence technologies, and it can be regarded as a kind of multilayer feedforward neural network. An essence of deep learning is information propagation through layers. This suggests that there is a connection between deep neural networks and dynamical systems in the sense that information propagation is explicitly modeled by the time evolution of dynamical systems. In this study, we perform pattern recognition based on the optimal control of continuous-time dynamical systems, which is suitable for physical hardware implementation. The learning is based on the adjoint method to optimally control dynamical systems, and the deep (virtual) network structures based on the time evolution of the systems are used for processing input information. As a key example, we apply the dynamics-based recognition approach to an optoelectronic delay system and demonstrate that the use of the delay system allows for image recognition and nonlinear classifications using only a few control signals. This is in contrast to conventional multilayer neural networks, which require a large number of weight parameters to be trained. The proposed approach provides insight into the mechanisms of deep network processing in the framework of an optimal control problem and presents a pathway for realizing physical computing hardware.