Mathematical Psychology and Psychophysiology

Stephen Grossberg

• Publisher: Psychology Press
• Year: 2014
• eBook ISBN: 9781317769637
• Topic: Psicología
• Subtopic: Historia y teoría en psicología

Mathematical Psychology and Psychophysiology promotes an understanding of the mind and its neural substrates by applying interdisciplinary approaches to issues concerning behavior and the brain. The contributions present model from many disciplines that share common, conceptual, functional, or mechanistic substrates and summarize recent models and data from neural networks, mathematical genetics, psychoacoustics, olfactory coding, visual perception, measurement, psychophysics, cognitive development, and other areas.

The contributors to Mathematical Psychology and Psychophysiology show the conceptual and mathematical interconnectedness of several approaches to the fundamental scientific problem of understanding mind and brain. The book's interdisciplinary approach permits a deeper understanding of theoretical advances as it formally structures a broad overview of the data.

Adaptive Resonance in Development, Perception and Cognition

Stephen Grossberg¹

1. Introduction. Several of the best physicists of the last half of the nineteenth century were also distinguished psychologists or physiologists. The contributions of Helmholtz, Maxwell, and Mach to perception are notable examples of this productive interdisciplinary activity (Boring [1950], Koenigsberger [1906], Campbell and Garnett [1882], Ratliff [1965]). Why then did not interdisciplinary studies, based on these inspiring successes, flourish at the beginning of the twentieth century?

One reason lies in the nature of psychophysiological phenomena. The mathematics of traditional physics has been centered in linear and stationary concepts, whereas the data of psychophysiology are often nonlinear and nonstationary. The great revolutions of twentieth century physics were supported by nineteenth century mathematics, but the emergent concepts of psychophysiology, from the very outset, lead to new mathematics. We seem to be experiencing the type of scientific revolution wherein new intuitive physical concepts and new mathematics must both be simultaneously developed, each fertilizing the other. Such scientific developments bring with them special challenges, but also special intellectual rewards.

In this article, I shall discuss nonlinear and nonstationary concepts that arise from consideration of some basic questions about brain design, and I will indicate how the answers help to unify several of the contributions reported elsewhere in the book. These questions include: How can an organism’s adaptive mechanisms be stable enough to resist environmental fluctuations which do not alter its behavioral success, but plastic enough to change rapidly in response to environmental demands that do alter its behavioral success? How is a balance between stability and adaptability achieved in a nonstationary environment? More simply expressed, how do internal representations of the environment develop through experience and thereafter maintain themselves? In particular, how are coding errors corrected, or adaptations to a changing environment effected, if individual nerve cells cannot detect that these errors or changes have occurred?

I will indicate how limitations in the information available to individual cells can be overcome when the cells act together in suitably designed feedback networks. In these networks, nonlinear competition between feedforward data patterns and learned feedback templates, or expectancies, helps to stabilize the developing code. This competition triggers events that buffer already committed populations against continual erosion by incompatible environmental fluctuations without sacrificing the adaptability of uncommitted populations. The buffering mechanism sets the stage for hypothesis testing and fast parallel search for uncommitted populations.

Environmental events lead to resonant activity within the system when their feedforward data and feedback templates reach concensus through a matching process. The resonant state embodies the perceptual event, or attentional focus, and its amplified and sustained activities are capable of driving slow adaptive changes in system structure. In other words, resonant activity within the short term memory (STM) system causes alterations in long term memory (LTM). These LTM changes, in turn, alter the resonant STM patterns, and the cycle continues until STM and LTM equilibrate. This dynamic exchange between STM and LTM is called an adaptive resonance. The “code” of a network is suggested to be the set of stable resonances which the network can support in response to a prescribed input environment (Grossberg [1976a], [1976b], [1978a], [1980a]).

Many adult perceptual and cognitive properties emerge within this framework as manifestations of the developmental mechanisms that are needed to ensure a balance between code stability and adaptability. Adaptive resonances are also suggested to be functional coding units in nonneural cellular tissues and play a prominent role in efforts to discover a universal developmental code (Grossberg [1978b]).

This article is built around a thought experiment that shows us, in simple stages, how to build up these nonlinear feedback networks. The thought experiment does this by indicating that several principles of neural design are needed to construct the networks. Each principle solves an environmentally imposed problem to which a surviving species must adapt. The mechanisms that realize each principle imply a variety of psychophysiological and pharmacological properties.

An important aspect of understanding brain design is to realize which data properties are consequences of which principles. Wherever we can recognize a general principle at work in a given body of data, we can compare and contrast these data with other data wherein the same principle is operatin...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Preface
• List of Contributors
• The visual system does a crude Fourier analysis of patterns
• Invariant properties of masking phenomena in psychoacoustics and their theoretical consequences
• A neural mechanism for generalization over equivalent stimuli in the olfactory system
• Differential equations for the development of topological nerve fibre projections
• Normal and abnormal signal patterns in nerve cells
• The law of large numbers in neural modelling
• Adaptive resonance in development, perception and cognition
• Psychophysiological substrates of schedule interactions and behavioral contrast
• Sociobiological variations on a Mendelian theme
• A “psychological” proof that certain Markov semigroups preserve differentiability
• Axiomatic measurement theory
• Optimal decision rules for some common psychophysical paradigms
• Mathematical models of binocular vision
• Reaction time distributions predicted by serial self-terminating models of memory search