Noisy Dynamical Artificial Feed-Forward Neural Networks

We establish a foundation for developing quantum neural networks that satisfy the classical-quantum correspondence principle, i.e., recover a classical neural network as the classical limit of the quantum neural network. Specifically, we extend a standard electrical-circuit formulation for dynamical neural networks to include non-reciprocal coupling and stochasticity of the electrical current. We then show that our extension to this model yields feedforward, which is needed to achieve an effective neural network. Furthermore, we validate our model and resultant numerical simulations by comparing special cases of our solutions against standard solutions of artificial neural networks. A key novelty in our approach is that we employ stochastic nonlinear differential equations rather than the standard nonlinear ordinary differential equations and we show equivalence of our approach to a Fokker-Planck equation. Our development of a noisy dynamical artificial feed-forward network is significant as a step towards feed-forward quantum networks where the noise is replaced by a quantum-state approach.