Scaling in a Hierarchical Unsupervised
Zoubin Ghahramani, Alexander Korenberg and Geoffrey E.
Gatsby Computational Neuroscience Unit
University College London
A persistent worry with computational models of unsupervised
learning is that learning will become more difficult as the problem is scaled. We
examine this issue in the context of a novel hierarchical, generative model that can be
viewed as a non-linear generalization of factor analysis and can be implemented in a
neural network. The model performs perceptual inference in a probabilistically
consistent manner by using top-down, bottom-up and lateral connections. These
connections can be learned using simple rules that require only locally available
information. We first demonstrate that the model can extract a sparse, distributed,
hierarchical representation of global disparity from simplified random-dot stereograms.
We then investigate some of the scaling properties of the algorithm on this problem
and find that : (1) increasing the image size leads to faster and more reliable learning;
(2) Increasing the depth of the network from one to two hidden layers leads to better
representations at the first hidden layer, and (3) Once one part of the network has
discovered how to represent disparity, it 'supervises' other parts of the network, greatly
speeding up their learning.
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