JOSE@LATOUR.ARPA (04/20/87)
[Forwarded from the Neuron Digest by Laws@STRIPE.SRI.COM.] Knowledge Representation in Connectionist Networks Stephen Jose Hanson and David J. Burr Bell Communications Research Morristown, New Jersey 07960 Abstract Much of the recent activity in connectionist models stems from two important innovations. First, a layer of independent, modifiable units (hidden layer) that can model the statistics of the domain and in turn perform significant associative mapping between stimulus pairs. Second, a learning rule that dynamically creates representation in the hidden layer based upon constraints from a teacher signal. Both Boltzmann machine and back-propagation models share these two innovations and interestingly ones that were apparently well known by Rosenblatt[14]. Although presently, many complex perceptual and cognitive models have been constructed using these methods the exact computational nature of the networks in terms of their clustering, partitioning, and generalization behavior is not well understood. In this paper we present a uniform view of the computational power of multi-layered learning (MLL) models. We show that MLL models represent knowledge by applying Boolean combination rules to partition the problem space into regions. A by-product of these rules is that knowledge is represented as distributed patterns of activation in the hidden layers. Their partitioning capability is related to both the neural device model and the network complexity in terms of numbers and layers of neurons. The device model determines the shape of an elementary boundary segment and the network determines how to combine the segments into region boundaries. For continuous problem spaces two hidden layers are sufficient to form arbitrary regions (or Boolean functions) in the space, and for binary-valued spaces a single layer suffices. Finally we show that networks can produce probabilistic combination rules which closely approximate the Bayes risk. You can get a copy of this paper by replying to this message or writing to jose@bellcore or djb@bellcore, comments appreciated.