Invertible generalized synchronization: A putative mechanism for implicit learning in biological and artificial neural systems (1807.05214v2)

Abstract: Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their governing equations. The brain is able to learn the dynamic nature of the physical world via experience; analogously, artificial neural systems can learn the long-term behavior of complex dynamical systems from data. Yet, precisely how this implicit learning occurs remains unknown. Here, we draw inspiration from human neuroscience and from reservoir computing to propose a first-principles framework explicating putative mechanisms of implicit learning. Specifically, we show that an arbitrary dynamical system implicitly learns other dynamical attractors by embedding them into its own phase space through invertible generalized synchronization. By sustaining the embedding through fine-tuned feedback loops, the arbitrary dynamical system can imitate the attractor dynamics it has learned. To evaluate the mechanism's relevance, we construct several distinct neural network models that adaptively learn and imitate multiple attractors. We observe and explain the emergence of 5 distinct phenomena reminiscent of cognitive functions: (i) imitating a dynamical system purely from learning the time series, (ii) learning multiple attractors by a single system, (iii) switching among the imitations of multiple attractors, either spontaneously or driven by external cues, (iv) filling-in missing variables from incomplete observations of a learned dynamical system, and (v) deciphering superimposed input from different dynamical systems. Collectively, our findings support the notion that artificial and biological neural networks can learn the dynamic nature of their environment, and systems within their environment, through the mechanism of invertible generalized synchronization.