Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

5 Complexity of Learning

J. Stephen Judd

Siemens Corporate Research

Learning is a quintessential ability of brains, and it is a major focus of much connectionist research. Unfortunately, the learning algorithms reported in the literature so far are all unacceptably slow in large networks. Although it is clear that we need to be able to scale up our applications to much bigger networks, it is not at all clear how to achieve this. Many researchers view this as the most pressing challenge for current connectionist research.

Currently, the major domain of design freedom in artificial neural networks is in the specification of which nodes are connected to which other nodes, but there seem to be few principles or methodologies for designing the specific connectivity patterns in these networks. Network designs in the literature seem to have been rather ad hoc constructions for specific experiments. The discovery of well-grounded and universal design principles would assist the development of artificial neural networks and strengthen links to biological brain structure. Such design principles would arise from consideration of many types of constraints, but this chapter focuses only on a particular type of learning issue.


1. LEARNING

Neural networks are typically operated in two modes--the so-called loading or learning mode wherein data are stored into the permanent memory base and the retrieval mode wherein those associative data are recalled from memory. Figure 5.1 depicts the general paradigm. During retrieval, each computing node calculates an output value some simple rule, such as a threshold function on the weighted sum of its current inputs. This simple scalar (or perhaps even binary) value becomes the signal transmitted to other such simple nodes. For simplicity, this chapter discusses

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