Learning in networks of structured hypercubes
This thesis is an investigation into neural networks whose units are defined by a set of values at the corners of a hypercube; this includes the Boolean functions as a special case. One of the main objectives was the development of training algorithms for nets with so-called hidden units. Also addressed is the problem of training set generalization, the relation between hypercube based units and the more usual threshold logic unit, and issues of implementation. There are two main points of departure that initiate training algorithm development. The first is an interpretation of net function in geometric terms with respect to the natural Hamming distance topology on the hypercube. This leads to the idea that generalization is fostered by the creation of clusters of like valued sites on the cube, and to an understanding of the role of hidden units as removing site value conflict and cluster fragmentation on the visible nodes. Indeed it was this insight that led to the use of the term hypercube in the node description. It is shown that the location of cluster centers may be optimized by treating them as if they were particles with an interparticle potential energy function. A method is discussed for cluster generation which introduces external input via a bit-stream, with the final output depending non-linearly on the stream contents; thus noise is introduced automatically in a controlled way, and clusters may be generated around known centers as the input changes from one training pattern to the next. The second main starting point centers on a closed expression for Boolean functionality. This may be extended to define an analogue node type which, because of the continuous nature of the variables now involved, avails itself of mathematical analysis, and hence to the proof of convergence under training paradigms such as back-propagation and reward penalty.
- Research Organization:
- Brunel Univ., Uxbridge (UK)
- OSTI ID:
- 6223738
- Resource Relation:
- Other Information: Thesis (Ph.D)
- Country of Publication:
- United States
- Language:
- English
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