# Hyperbolic Tangent Functions and Neural Networks

## Marimuthu Murugananth

The hyperbolic tangent is a common transfer function in neural networks. One reason is that it is a very flexible, non-linear function. It is also continuous and differentiable. The intention here is to illustrate its flexibility.

## Example 1

This example illustrates the flexibility of a hyperbolic tangent in which the output *y* is expressed as a function of two inputs *x*_{1} and *x*_{2} . The shape of the surface changes as the weights *w*_{1
} and *w*_{2} are varied. The equation below is the actual function being plotted.

Click to start the simulation

## Example 2

This example illustrates how combining a variety of hyperbolic tangents gives even greater flexibility. There output *y* is expressed as a function of two inputs *x*_{1} and *x*_{2}. The shape of the surface changes dramatically as the weights *w*_{1} and *w*_{2} are varied in the range 0-10. The equation below is the actual function being plotted.

A neural network with four hyperbolic tangents would be said to have four *hidden units*.

Click to start the simulation

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## References