Euclidean Contractivity of Neural Networks With Symmetric Weights

Feedforward neural networks with constrained weights

On Neural Networks with Minimal Weights

Linear threshold elements are the basic building blocks of artificial neural networks. A linear threshold element computes a function that is a sign of a weighted sum of the input variables. The weights are arbitrary integers; actually, they can be very big integers-exponential in the number of the input variables. However, in practice, it is difficult to implement big weights. In the present l...

Asymptotic Description of Neural Networks with Correlated Synaptic Weights

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe the asymptotic law of the network when the number of neurons goes to infinity. We introduce the process-level empirical measure of the trajectories of the s...

On the VC-dimension of neural networks with binary weights

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committeeand the parity-machine with weights restricted to values ±1. For binary inputs, the VC-dimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that ar...

Capacity of Two-Layer Feedforward Neural Networks with Binary Weights

The lower and upper bounds for the information capacity of two-layer feedforward neural networks with binary interconnections, integer thresholds for the hidden units, and zero threshold for the output unit is obtained through two steps. First, through a constructive approach based on statistical analysis, it is shown that a specifically constructed (N 2L 1) network with N input units, 2L hidde...