Ph. D. Candidate
The University of Memphis
Department of Computer Science
Computational Neurodynamics Lab
Overview of K Sets
K sets have been popularized by Walter J. Freeman in his book "Mass Action in the Nervous System" (1975). The main thesis of the book is that the key for understanding cognitive processes is in studying dynamics of neural populations, and not individual neurons. Thus the EEG's and averaged electrical activity of the brain must be used as state variables of brain models, as opposed to spike counts and local membrane potentials.
Decades of neurophysiologic experiments yielded the following key characteristics of neural masses.
A) Population of non-interacting neurons is described by a second order linear differential equation with averaged pulse density as state variable and the coefficients determined by curve fitting to the experimental data. This population model is called K0 set.
B) Transfer function of a population of non-interacting neurons is an asymmetric sigmoid. The parameters of this sigmoid were determined by curve fitting as well.
C) Interacting populations of neurons can be modeled as networks of K0 sets with positive and negative connections between them. Such networks are described by systems of non-linearly coupled ODE's. Depending on the neural population being modeled, such networks are called KII sets and KIII sets. KIII set with appropriately tuned parameters can produce complex aperiodic dynamics similar to what is observed in EEG's
D) Theory of "Chaotic Brain" was proposed, which considers the brain as non-convergent dynamical system with many strange attractors (wikipedia) which represent mental concepts and memories. Formation of these attractors is through Hebbian learning (wikipedia). The search and retrieval is achieved with the help of "phase transitions" mechanism. This mechanism is also related to the concept of chaotic itinerancy.
K Sets as new neural network type
After the initial KIII models demonstrated brain-like dynamics it became possible to use them for solving practical problems, namely classification. They can also be used in time series prediction (see K-Toolbox page). Several KIII networks form a KIV network which models multiple modalities of perception. Such networks can be used for navigation problems.