Stochastic Dynamics

Having understood the power of deterministic analog recurrent neural networks, we now turn our attention to networks that exhibit stochastic and random behavior. Randomness is a basic characteristic of large distributed systems. It may result from the activity of the individual agents, from unpredictable changes in the communication pattern among the agents, or even just from the different update paces. All previous work that examined stochasticity in networks, e.g., [vN56, Pip90, Adl78, Pip88, Pip89, DO77a, DO77b], studied only acyclic architectures of binary gates, while we study general architectures of analog components. Due to these two qualitative differences, our results are totally different from the previous ones, and require new proof techniques.