Feed-Forward Neural Networks for Failure Mechanics Problems

Solving arithmetic problems using feed-forward neural networks

We design new feed-forward multi-layered neural networks which perform di erent elementary arithmetic operations, such as bit shifting, addition of N p-bit numbers, and multiplication of two n-bit numbers. All the structures are optimal in depth and are polinomialy bounded in the number of neurons and in the number of synapses. The whole set of synaptic couplings and thresholds are obtained exa...

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...

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.

Using artificial neural networks for solving chemical problems Part I. Multi-layer feed-forward 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 ...