Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?
Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.
We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between pre- and postsynaptic spikes. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed, if the integral of the learning window is negative. A negative integral corresponds to anti-Hebbian' learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and
anti-Hebbian' rules is questionable since learning is driven by correlations on the time scale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. Whereas a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.
Chargement
Chargement
Chargement
Chargement
Chargement
Hebbian'') learning rule at the spike level is formulated, mathematically analyzed, and compared with learning in a firing-rate description. As for spike coding, we take advantage of a
learning window'' that describes the effect of timing of pre- and postsynaptic spikes on synaptic weights. A differential equation for the learning dynamics is derived under the assumption that the time scales of learning and spiking dynamics can be separated. Formation of structured synapses is analyzed for a Poissonian neuron model which receives time-dependent stochastic input. It is shown that correlations between input and output spikes tend to stabilize structure formation. With an appropriate choice of parameters, learning leads to an intrinsic normalization of the average weight and the output firing rates. Noise generates diffusion-like spreading of synaptic weights.Nicolas Frémaux, Wulfram Gerstner, Walter Senn, Eleni Vasilaki
Wulfram Gerstner, Jean-Pascal Théodor Pfister, Taro Toyoizumi