Bookraft

Neural Networks: A Comprehensive Foundation is an example of science meeting a barrior. Forty years ago, in a communications science class at the University of Michigan I heard Professor Simons tell our class that the problem of human neural circuitry and how memory works would be solved within the decade. In addition, the basic math and wiring behind human neural networks would be elucidated first in AIN-Artificial Intelligence Networks and then mapped onto the brain with appropriate adjustments/refinements.

Well that mapping has yet to occur. But the theory of Neural Networks is rich and this book, some thirty years later describes the huge range of thinking and experimentation on how circuits can get better and learn based on inputs and feedback on those derived inputs.
But the going is perilous - take this section on Performance Measures for Perceptrons:
What then is a suitable performance measure for the single layer perceptron? An obvious choice would be the average probability of classification error, defined as the the average probability of the perceptron making a decision in favor of a particular class when the input vector is actually dramwn from some other class. Unfortunately, such a performance measure does not lend itself readily to the analytic derivation of a learning algorithm.

This is typical of what it can be like slogging it out in the trenches of science. But I bring this up because I want to show that indeed science does not only look for but attempt to elucidate performance measures (in this case, analytic but based on a strong analog, the perceptron, to basic organic neural circuits). The problem in neuroscience is that it is exeedingly hard to measure basic operations of brain functioning. Even the recent advances of PET and other scanning technologies work on a gross structural level where answers are needed on small cellular circuit performance but still in a functionally rich environ.

But this book is full of various models of circuit based learning and limits. Chapter 9 on the Self Organizing Systems looks at the big picture and tries to define some constraints and expectations on what will have to take place in "biological learning systems" The next chapter on Self Organizing Systems II looks at models of Competitive Learning - and this posits several methods of determing the nature of competitive processes, that is specialized areas vying for the opportunity to act on inputs. Again the authors map onto the human brain and known neural specialization (Hebb's famous Homunculi) and then sees how these map to mathematical neural models.

In sum after reading this book it becomes clear how sophisticated and yet crude the math neural models are in explaining basic human neural processes. Yet again, I believe that Professor Simons was right just delayed by 100 or more years. Yes, math neural models will help to elucidate how the brain works; just that the basic explanatory mappings likely won't occur in his or my lifetimes.