| ### Chapter 3 - Single-Layer Networks
Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks
Russell D. Reed and Robert J. Marks II
Copyright © 1999 Massachusetts Institute of Technology

# Chapter 3: Single-Layer Networks

## Overview

Single-layer networks (figure 3.1) have just one layer of active units. Inputs connect directly to the outputs through a single layer of weights. The outputs do not interact so a network with Nout outputs can be treated as Nout separate single-output networks. Each unit (figure 3.2) produces its output by forming a weighted linear combination of its inputs which it then passes through a saturating nonlinear function

(3.1) |

(3.2) |

This can be expressed more compactly in vector notation as

(3.3) |

where x and w are column vectors with elements xj and wj,and the superscript T denotes the vector transpose. In general, f is chosen to be a bounded monotonic function. Common choices include the sigmoid function f(u) = 1/(1 + e-u) and the tanh functions. When f is a discontinuous step function, the nodes are often called linear threshold units (LTU). Appendix D mentions other possibilities.

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