We consider a statistical framework in which recurrent networks of spiking neurons learn to generate spatio-temporal spike patterns. Given biologically realistic stochastic neuronal dynamics we derive a tractable learning rule for the synaptic weights towards hidden and visible neurons that leads to optimal recall of the training sequences. We show that learning synaptic weights towards hidden neurons significantly improves the storing capacity of the network. Furthermore, we derive an approximate online learning rule and show that our learning rule is consistent with Spike-Timing Dependent Plasticity in that if a presynaptic spike shortly precedes a postynaptic spike, potentiation is induced and otherwise depression is elicited.

Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a fixed computational operation in a network, this seems like a most unacceptable degree of added noise. We suggest an alternative theory according to which short term synaptic plasticity plays a normatively-justifiable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quantity that contains all the critical information, namely its membrane potential. We suggest that one key task for a synapse is to solve the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives and prior expectations, as in a recursive filter. We show that short-term synaptic depression has canonical dynamics which closely resemble those required for optimal estimation, and that it indeed supports high quality estimation. Under this account, the local postsynaptic potential and the level of synaptic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential fluctuations and the form of spiking non-linearity should be related to the properties of short-term plasticity in any particular cell type.

While classical experiments on spike-timing dependent plasticity analyzed synapticchanges as a function of the timing of pairs of pre-and postsynaptic spikes, more recent experiments also point to the effect of spike triplets. Here we develop a mathematical framework that allows us to characterize timing based learning rules. Moreover, we identify a candidate learning rule with five variables (and 5 free parameters) that captures a variety of experimental data, including the dependence of potentiation anddepression upon pre-and postsynaptic firing frequencies. The relation to the Bienenstock-Cooper-Munro rule as well as to some timing-based rules is discussed.

While classical experiments on spike-timing dependent plasticity analyzed synaptic changes as a function of the timing of pairs of pre-and postsynaptic spikes, more recent experiments also point to the effect of spike triplets. Here we develop a mathematical framework that allows us to characterize timing based learning rules. Moreover, we identify a candidate learning rule with five variables (and 5 free parameters) that captures a variety of experimental data, including the dependence of potentiation and depression upon pre-and postsynaptic firing frequencies. The relation to the Bienenstock-Cooper-Munro rule as well as to some timing-based rules is discussed.

We derive an optimal learning rule in the sense of mutual information maximization for a spiking neuron model. Under the assumption of small fluctuations of the input, we find a spike-timing dependent plasticity (STDP)function which depends on the time course of excitatory postsynaptic potentials (EPSPs) and the autocorrelation function of the postsynaptic neuron. We show that the STDP function has both positive and negative phases. The positive phase is related to the shape of the EPSP while the negative phase is controlled by neuronal refractoriness.