As noted previously, Hinton has recently shown interesting results concerning the benefits of adding ‘dropouts’ in neural networks during learning (see : Improving neural networks by preventing co-adaptation of feature detectors).

Again, one of the claimed benefits of using an explicit dropout rate of 50% is that for a doubling of required processing (since only approximately half the neurons are available for training for any given training iteration, the number of training cycles should approximately double) the training is actually occuring across the power set of possible neuron networks (with a huge amount of weight sharing).

This argument is similar to the ‘hyperplane sampling’ argument from Genetic Algorithms (GAs) in the early 1990s.

Hyper-Planes

In GAs, one argument that was developed to show why genetic crossover seemed so much more effective than the linear sampling rate would suggest is that each fitness measurement for an individual could be thought of as implicitly sampling estimates of fitness from all of the ‘hyperplanes’ that had the particular individual in common. i.e. 1 measurement of an N-bit individual would provide data relevant to the fitness of all 2^N hyperplanes.

As a concrete example, computing the fitness of a single point - fitness('010101')- implictly gives data for estimates of the fitness of many other hyperplanes : E{fitness('*10101')}, E{fitness('0*0101')}, E{fitness('010***')}, etc. (where ‘*’ stands for a wild-card set along any particular axis).

But…

On its face, the hyper-planes argument always sounded a little too-good-to-be-true. And the fact that GA people are not beating the drum even more loudly now than two decades ago suggests that there may be less mileage in this line of reasoning than it first appeared.

It’s possible the “2^N networks for 2xN work” idea has merit - but be wary…