On the effect of analog noise in discrete-time analog computations
We introduce a model for analog computation with discrete time in the presence
of analog noise that is flexible enough to cover the most important concrete
cases, such as noisy analog neural nets and networks of spiking neurons. This
model subsumes the classical model for digital computation in the presence of
noise. We show that the presence of arbitrarily small amounts of analog noise
reduces the power of analog computational models to that of finite automata,
and we also prove a new type of upper bound for the VC-dimension of
computational models with analog noise.
Reference: W. Maass and P. Orponen.
On the effect of analog noise in discrete-time analog computations.
Neural Computation, 10:1071-1095, 1998.