March 7, 2017

Artificial Neural Networks and Information Theory by Fyfe C.

By Fyfe C.

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5. 1: Each column represents the values input to a single input neuron. Each row represents the values seen by the network at any one time. 2: Results from the simulated network and the reported results from Oja et al. The left matrix represents the results from the negative feedback network (see next Chapter), the right from Oja’s Subspace Algorithm. Note that the weights are very small outside the principal subspace and that the weights form an orthonormal basis of this space. 1 are shown in bold font.

The entropy of a Gaussian random variable is totally determined by its variance. We will later see that this is not true for other distributions. 4 Information Theory and the Neuron Linsker has analysed the effect of noise on a neuron’s processing capabilities. He begins by stating the Infomax principle (we will discuss his network in a later chapter) which can be stated approximately as: it is the responsibility of the neurons in the output layer of a network to jointly maximise the information at the outputs about the input activations of the network.

2) the latter being the learning mechanism. Here yi is the output from neuron i, xj is the j th input, and wij is the weight from xj to yi . α is known as the learning rate and is usually a small scalar which may change with time. Note that the learning mechanism says that if xj and yi fire simultaneously, then the weight of the connection between them will be strengthened in proportion to their strengths of firing. 1: A one layer network whose weights can be learned by simple Hebbian learning.

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