A theory of neural networks
Igor Aleksander · 2003
This chapter describes the writer's past contribution in developing McCulloch's models of neural activity. Central to this was the creation of an algebraic formulation called ‘Neuronic Equations’ (NE). This both advanced and generalized McCulloch's treatment, liberating the discussion to include time behaviour, learning, and the intellectual framework for what might constitute a ‘thinking machine’. Much work has been done since this was first published in the Journal of Theoretical Biology in April 1961, leading to a variety of quantitative results. Amongst other things, it was found that NEs could be solved exactly as an inverse problem: given a prescribed behaviour, determine the net that generates it. Such explicit solutions include the class of NE that describe cellular automata and a precise specification of behaviour in terms of cycles, transients and singularities. The results thus obtained, provide a natural framework for the discussion of contemporary concerns in neural computing. The Appendix directs the reader (through a bibliography) towards discussions of application to linguistics, pattern recognition and the mature multilevel structures.