Constraints on learning in dynamic synapses

Some constraints intrinsic to unsupervised learning in at tractor neural networks (ANN) are discussed. Hebbian type learning is discussed in a network whose synapses are analog, dynamic variables, with a fixed finite number of states that are stable on long time scales. It is shown that if the patterns to be learned are random words of ±1 bits then in the limit of slow presentation, the network can learn at most O(ln N) patterns in N neurons. Going beyond the logarithmic contraint requires stochastic learning of patterns and low coding rate.