Physical learning in evolving finite state machines

Finite state machines (FSMs), a system composed of a finite number of states with transitions between them, are prevalent in living and nonliving matter. In the latter case, consider a solid particle packing that has been cyclically sheared such that local, hysteretic rearrangements of particles above some threshold strain trigger other local, hysteretic rearrangement of particles some distance away. The non-rearranging particles in between these rearranging regions govern their interactions. Sequences of such triggers can be represented as a FSM given a finite number of possible rearrangements. As for perhaps an unexpected example of a living FSM, consider chromatin in the cell nucleus as a correlated, polymeric fluid populated with local regions of chromatin crosslinkers that can rearrange above some threshold strain and also exhibit hysteresis. In this case, the interactions between the chromatin crosslinker regions are governed by the surrounding active, correlated polymeric fluid. Using physics-based genetic algorithms to evolve these physical FSMs, we explore their potential for learning as the couplings governing the interactions between the rearranging regions are modified. Our approach complements gradient-based methods in physical learning and may reveal new underlying physical principles of learning through the exploration of finite state machine space with lower expressivity, as compared to gradient-based methods, but enhanced simplicity.