Adaptation to criticality through organizational invariance in embodied agents

Many biological and cognitive systems do not operate deep within one or other regime of activity. Instead, they are poised at critical points located at phase transitions in their parameter space. The pervasiveness of criticality suggests that there may be general principles inducing this behaviour, yet there is no well-founded theory for understanding how criticality is generated at a wide span of levels and contexts. In order to explore how criticality might emerge from general adaptive mechanisms, we propose a simple learning rule that maintains an internal organizational structure from a specific family of systems at criticality. We implement the mechanism in artificial embodied agents controlled by a neural network maintaining a correlation structure randomly sampled from an Ising model at critical temperature. Agents are evaluated in two classical reinforcement learning scenarios: the Mountain Car and the Acrobot double pendulum. In both cases the neural controller appears to reach a point of criticality, which coincides with a transition point between two regimes of the agent's behaviour. These results suggest that adaptation to criticality could be used as a general adaptive mechanism in some circumstances, providing an alternative explanation for the pervasive presence of criticality in biological and cognitive systems.

Criticality as It Could Be: organizational invariance as self-organized criticality in embodied agents

This paper outlines a methodological approach for designing adaptive agents driving themselves near points of criticality. Using a synthetic approach we construct a conceptual model that, instead of specifying mechanistic requirements to generate criticality, exploits the maintenance of an organizational structure capable of reproducing critical behavior. Our approach exploits the well-known principle of universality, which classifies critical phenomena inside a few universality classes of systems independently of their specific mechanisms or topologies. In particular, we implement an artificial embodied agent controlled by a neural network maintaining a correlation structure randomly sampled from a lattice Ising model at a critical point. We evaluate the agent in two classical reinforcement learning scenarios: the Mountain Car benchmark and the Acrobot double pendulum, finding that in both cases the neural controller reaches a point of criticality, which coincides with a transition point between two regimes of the agent's behaviour, maximizing the mutual information between neurons and sensorimotor patterns. Finally, we discuss the possible applications of this synthetic approach to the comprehension of deeper principles connected to the pervasive presence of criticality in biological and cognitive systems.

Learning Criticality in an Embodied Boltzmann Machine

Many biological and cognitive systems do not operate deep into one or other regime of activity. Instead, they exploit critical surfaces poised at transitions in their parameter space. The pervasiveness of criticality in natural systems suggests that there may be general principles inducing this behaviour. However, there is a lack of conceptual models explaining how embodied agents propel themselves towards these critical points. In this paper, we present a learning model driving an embodied Boltzmann Machine towards critical behaviour by maximizing the heat capacity of the network. We test and corroborate the model implementing an embodied agent in the mountain car benchmark, controlled by a Boltzmann Machine that adjust its weights according to the model. We find that the neural controller reaches a point of criticality, which coincides with a transition point of the behaviour of the agent between two regimes of behaviour, maximizing the synergistic information between its sensors and the hidden and motor neurons. Finally, we discuss the potential of our learning model to study the contribution of criticality to the behaviour of embodied living systems in scenarios not necessarily constrained by biological restrictions of the examples of criticality we find in nature.