Stochastic binary synapses having sigmoidal cumulative distribution functions for unsupervised learning with spike timing-dependent plasticity

Spike timing-dependent plasticity (STDP), which is widely studied as a fundamental synaptic update rule for neuromorphic hardware, requires precise control of continuous weights. From the viewpoint of hardware implementation, a simplified update rule is desirable. Although simplified STDP with stochastic binary synapses was proposed previously, we find that it leads to degradation of memory maintenance during learning, which is unfavourable for unsupervised online learning. In this work, we propose a stochastic binary synaptic model where the cumulative probability of the weight change evolves in a sigmoidal fashion with potentiation or depression trials, which can be implemented using a pair of switching devices consisting of serially connected multiple binary memristors. As a benchmark test we perform simulations of unsupervised learning of MNIST images with a two-layer network and show that simplified STDP in combination with this model can outperform conventional rules with continuous weights not only in memory maintenance but also in recognition accuracy. Our method achieves 97.3% in recognition accuracy, which is higher than that reported with standard STDP in the same framework. We also show that the high performance of our learning rule is robust against device-to-device variability of the memristor's probabilistic behaviour.