An Infinite Restricted Boltzmann Machine
This addresses a hyperparameter tuning issue for researchers and practitioners using RBMs, though it is incremental as it builds on existing RBM frameworks.
The paper tackles the problem of specifying the number of hidden units in restricted Boltzmann machines by introducing an infinite RBM with an adaptive hidden layer that grows during training, showing competitive performance without tuning hidden layer size.
We present a mathematical construction for the restricted Boltzmann machine (RBM) that doesn't require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, thanks to a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behaviour of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size.