# Martin Krupa - Université Côte d'Azur - Keywords: associative memory, mathematical modelling

Prediction is the ability of the brain to quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli, and other experiments show that prime-target relations arise in the process of long term memory formation. The classical modelling paradigm is that long term memories correspond to stable steady states of a Hopfield network with Hebbian connectivity. Experiments show that short term synaptic depression (a phenomenon caused by depletion of a neurotransmitter) plays an important role in the processing of memories. This leads naturally to a computational model of sequential activation of concepts/memories, called latching dynamics; a stable state (prime) can become unstable and the system may converge to another transiently stable steady state (target). In this presentation we show how latching dynamics can be related to heteroclinic chains, that is sequences of transiently stable steady states joined by connecting orbits. The properties of such chains can be studied using the methods of dynamical systems. We show that noise and time scale separation play a fundamental role in the activation of latching dynamics in the context of heteroclinic chains. We also show that latching dynamics lacks robustness if a symmetric Hebbian rule is used to construct the connectivity matrix, and discuss possible modifications to the learning rule allowing for increased robustness of the phenomenon.