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

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, we have developed a simple and general model for the dynamics of an adaptive network with an additional meta-plastic mechanism, that we name “meta-reinforcement”, that varies the rate of Hebbian strengthening of its edge connections. 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. Most importantly, we show that meta-reinforcement allows the retrieval of the memorised path even when all weights have been reset, erasing all standard Hebbin memory from the network.