A Mathematical Analysis of Memory Lifetime in a simple Network Model of Memory

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to other signals considered as noise. The presentation of an external stimulus changes the state of the synapses in a network of binary neurons. Multiple presentations of a unique signal leads to its learning. Then, the presentation of other signals also changes the synaptic weight (during the forgetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as forgotten. We construct an estimator of the initial signal thanks to the synaptic currents. In our model, these synaptic currents evolve as Markov chains. We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is forgotten. We finally present numerical illustrations of our results