Meta-plasticity and memory in multi-level recurrent feed-forward networks

Abstract

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and sub-networks. To a first approximation, this memory can be modelled through a ``plastic'' Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multi-level network structures and ``meta-plastic'' effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional meta-plastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The meta-plastic term acts on a second network level in which edges are grouped together, simulating local, longer time-scale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a meta-plastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorisation) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the meta-reinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, meta-reinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.