T. Fink

The output distribution of a deep-layered machine with random logics exhibits a critical network depth, at which it is maximally biased.


In a deep-layered machine, each node in the network is a Boolean function of all the nodes below it. We derive the exact distribution of the global output given a random assignment of Boolean functions to the local nodes, and confirm our prediction through extensive experiments. As the network depth increases, the distribution changes in two ways: it becomes exponentially biased towards preferred outputs, and the outputs true and false dominate, eventually drowning out everything else. These opposing forces give rise to a critical network depth, at which the distribution is maximally biased.

Exact distribution of the output of a deep-layered machine