We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, the VC Dimension of analog neural networks with the sigmoid activation function $\sigma(y)=1/1+e^{-y}$ to be bounded by a quadratic polynomial in the ... more >>>

It is shown that high order feedforward neural nets of constant depth with piecewise polynomial activation functions and arbitrary real weights can be simulated for boolean inputs and outputs by neural nets of a somewhat larger size and depth with heaviside gates and weights from {-1,0,1\}. This provides the first ... more >>>

It has been known for quite a while that the Vapnik-Chervonenkis dimension (VC-dimension) of a feedforward neural net with linear threshold gates is at most O(w log w), where w is the total number of weights in the neural net. We show in this paper that this bound is in ... more >>>

We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog neural networks with the sigmoidal activation function $\sigma(y)=1/1+e^{-y}$ is bounded by a quadratic polynomial $O((lm)^2)$ in ... more >>>

Recently one has started to investigate the computational power of spiking neurons (also called ``integrate and fire neurons''). These are neuron models that are substantially more realistic from the biological point of view than the ones which are traditionally employed in artificial neural nets. It has turned out that the ... more >>>

Spiking neurons are models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal pattern of their activity. In a network of spiking neurons a new set of parameters becomes relevant which has no counterpart in traditional neural network models: the ... more >>>

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 ... more >>>

We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a large set. We show that many regular languages cannot be recognized by networks of this type, and we give a precise characterization ... more >>>

A neural network is said to be nonoverlapping if there is at most one edge outgoing from each node. We investigate the number of examples that a learning algorithm needs when using nonoverlapping neural networks as hypotheses. We derive bounds for this sample complexity in terms of the Vapnik-Chervonenkis dimension. ... more >>>

A simple extension of standard neural network models is introduced that provides a model for neural computations that involve both firing rates and firing correlations. Such extension appears to be useful since it has been shown that firing correlations play a significant computational role in many biological neural systems. Standard ... more >>>

In a great variety of neuron models neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks which contain units that multiply their inputs instead of summing them and, thus, allow inputs to interact nonlinearly. The class of multiplicative networks comprises such widely known ... more >>>

One of the most basic pattern recognition problems is whether a certain local feature occurs in some linear array to the left of some other local feature. We construct in this article circuits that solve this problem with an asymptotically optimal number of threshold gates. Furthermore it is shown that ... more >>>