Autonomous learning by simple dynamical systems with a discrete-time formulation

Abstract

We present a discrete-time formulation for the autonomous learning conjecture.The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.

The Relationship of Personality Traits with Metacognition: The Regulating Role of Mindfulness

“…In the literature, positive correlations were found between emotional instability and negative metacognitive beliefs (McEvoy & Mahoney, 2012;Sugiura, 2017; Van der Heiden, Melchior, Muris, Bouwmeester, Bos, & Van der Molen, 2010). In one study, emotional instability was positively related to anxiety, depression, negative self, and hostility (Bilen, 2017). Another study determined that emotionally unstable personality traits were positively related to anxiety, depression, negative self, somatization, and hostility.…”

Self-organizing dynamical networks able to learn autonomously

“…The formulation we present in this manuscript has the same scheme of parameter updated through a map as our previous discrete time model shown in ref. [27]. In effect, in both formulations we require that the time interval τ between updates be long enough to allow the system to reach a well-defined error value.…”

“…The main goal of this scheme is for the dynamical system to learn without the intervention of an external tutor. Already we have shown in previous works that this concept can be applied to different dynamical systems such as phase oscillators [26], feed-forward neural networks [27], and for gradient dynamics and control of oscillation death in Kuramoto-Tsuzuki systems of oscillators [28].…”