Figure 1
Introduction of stochastic S-STDP. (a) Schematics of S-STDP. While the synaptic weight update has exponential-like dependence on \({t}_{post}-{t}_{pre}\) in standard STDP (broken curves), S-STDP is characterised by a rectangular dependence (green line). Since an update takes place at the occurrence of a post-neuron's fire, we only consider the case of \({t}_{post}-{t}_{pre}>0\) for S-STDP. In the scheme of stochastic S-STDP with binary weights, the weight change \({\eta }_{+}\) and \({\eta }_{-}\) are read as the transition probabilities \(p\) from \(w=0\) to \(1\) for potentiation and \(q\) from \(1\) to \(0\) for depression, respectively. (b) Memory maintenance characteristics of learning with conventional stochastic S-STDP. The number of neurons that retain the digit memorised during the initial learning is plotted against the number of extra trainings (number of training samples presented for additional learning). Depression probability \(q\) is varied while potentiation \(p\) is fixed at 0.04. For comparison the characteristic of learning with deterministic S-STDP using continuous weights is shown as a thick line, for which we employ a linear weight-dependent update model33,37, where \(\Delta w={\eta }_{+}\left({w}_{max}-w\right)\) for potentiation and \(\Delta w={\eta }_{-}\left(w-{w}_{min}\right)\) for depression with \({\eta }_{+}=0.04\) and \({\eta }_{-}=0.008\), respectively. (c,d) Evolutions of expected weights for conventional stochastic S-STDP (c) and proposed "sigmoidal stochastic" S-STDP (d).
