Physical deep learning based on optimal control of dynamical systems

A central topic in recent artificial intelligence technologies is deep learning, which can be regarded as a multilayer feedforward neural network. An essence of deep learning is the information propagation through the layers, suggesting a connection between deep neural networks and dynamical systems, in the sense that the information propagation is explicitly modeled by the time-evolution of dynamical systems. Here, we present a pattern recognition based on 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 can be used for processing input information. As an example, we apply the dynamics-based recognition approach to an optoelectronic delay system and show that the use of the delay system enables image recognition and nonlinear classifications with only a few control signals, in contrast to conventional multilayer neural networks which require training of a large number of weight parameters. The proposed approach enables to gain insight into mechanisms of deep network processing in the framework of an optimal control problem and opens a novel pathway to realize physical computing hardware.