Synaptic connectivity in the brain is thought to encode the long-term memory of an organism. But experimental data point to surprising ongoing fluctuations in synaptic activity. Assuming that the brain computation and plasticity can be understood as probabilistic inference, one of the essential roles of noise is to efficiently improve the performance of optimization in the form of stochastic gradient descent. The strict saddle condition for synaptic plasticity is deduced and under such

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... noise can help escape from saddle points on high dimensional domains. The theoretical result explains the stochasticity of synapses and guides us how to make use of noise. Our simulation results manifest that in the learning and test phase, the accuracy of synaptic sampling is almost 20% higher than that without noise.