... observations

The complexity of the explanation is defined as the number of bits it takes to encode the observation using the model. In this case one would measure the total code length of the sources $\vec{s}(t)$, the parameters of the mapping and the noise $\vec{n}(t)$.

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... parameter

A hidden neuron will be shut off if all leaving weights are close to zero. Thinking in coding terms, it is easier for the network to encode this in one variance parameter than to encode it independently for all the weights.

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