Synaptic encoding of temporal contiguity

Often we need to perform tasks in an environment that changes stochastically. In these situations it is important to learn the statistics of sequences of events in order to predict the future and the outcome of our actions. The statistical description of many of these sequences can be reduced to the set of probabilities that a particular event follows another event (temporal contiguity). Under these conditions, it is important to encode and store in our memory these transition probabilities. Here we show that for a large class of synaptic plasticity models, the distribution of synaptic strengths encodes transitions probabilities. Specifically, when the synaptic dynamics depend on pairs of contiguous events and the synapses can remember multiple instances of the transitions, then the average synaptic weights are a monotonic function of the transition probabilities. The synaptic weights converge to the distribution encoding the probabilities also when the correlations between consecutive synaptic modifications are considered. We studied how this distribution depends on the number of synaptic states for a specific model of a multi-state synapse with hard bounds. In the case of bistable synapses, the average synaptic weights are a smooth function of the transition probabilities and the accuracy of the encoding depends on the learning rate. As the number of synaptic states increases, the average synaptic weights become a step function of the transition probabilities. We finally show that the information stored in the synaptic weights can be read out by a simple rate-based neural network. Our study shows that synapses encode transition probabilities under general assumptions and this indicates that temporal contiguity is likely to be encoded and harnessed in almost every neural circuit in the brain.