Many modern applications of the artificial neural networks ensue large number of layers making traditional digital implementations increasingly complex. Optical neural networks offer parallel processing at high bandwidth, but have the challenge of noise accumulation. We propose here a new type of neural networks using stochastic resonances as an inherent part of the architecture and demonstrate a possibility of significant reduction of the required number of neurons for a given performance accuracy. We also show that such a neural network is more robust against the impact of noise.