# On the effect of analog noise in discrete-time analog computations

### Abstract:

We introduce a model for noise-robust analog computations with discrete time
that is flexible enough to cover the most important concrete cases, such as
computations in noisy analog neural nets and networks of noisy spiking
neurons. 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.
In M. Mozer, M. I. Jordan, and T. Petsche, editors, *Advances in Neural
Information Processing Systems*, volume 9, pages 218-224. MIT Press
(Cambridge), 1997.