We study the learning of an external signal by a neural network and the time to URLet 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 URLetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as URLotten. 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 URLotten . We finally present numerical illustrations of our results.
We study the learning of an external signal by a neural network and the time to URLet it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses . Multiple presentations of a unique signal leads to its learning. Then, during the URLetting time, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal thanks to the synaptic currents and define by this way a probability of error . In our model, these synaptic currents evolve as Markov chains. We study the dynamics of these Markov chains and obtain a lower bound on the number of external stimuli that the network can receive before the initial signal is considered as URLotten (probability of error above a given threshold). Our results hold for finite size networks as well as in the large size asymptotic. They are based on a finite time analysis rather than large time asymptotic . We finally present numerical illustrations of our results.
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also changes the synaptic weight (during the URLetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as URLotten. We
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considered as URLotten (probability of error above a given threshold). Our results hold for finite size networks as well as in the large size asymptotic. They are based on a finite time analysis rather than large time asymptotic