Estimating Model Complexity of Feed-Forward Neural Networks

Estimating Model Complexity of Feed-Forward Neural Networks

Geometric Decomposition of Feed Forward Neural Networks

There have been several attempts to mathematically understand neural networks and many more from biological and computational perspectives. The field has exploded in the last decade, yet neural networks are still treated much like a black box. In this work we describe a structure that is inherent to a feed forward neural network. This will provide a framework for future work on neural networks ...

A Mathematical Model for Feed � Forward Neural Networks

We present a general model for di erentiable feed forward neural networks Its general mathemat ical description includes the standard multi layer perceptron as well as its common derivatives These standard structures assume a strong relationship between the network links and the neuron weights Our generalization takes advantage of the suppression of this assumption Since our model is especially...

Feed-forward neural networks: a geometrical perspective

The convex hull of any subset o f vertices of an n-dimensional hypercube contains no other vertex of the hypercube. This result permits the application of some theorems of n-dimensional geometry lo digital reed-forward neural networks. Also. the construction Of the convex hull is proposed as an alternative to more traditional learning algorithms. Some preliminary simulation results are reponed.

Some Theorems for Feed Forward Neural Networks

This paper introduces a new method which employs the concept of “Orientation Vectors” to train a feed forward neural network. It is shown that this method is suitable for problems where large dimensions are involved and the clusters are characteristically sparse. For such cases, the new method is not NP hard as the problem size increases. We ‘derive’ the present technique by starting from Kolmo...