The Mathematics of the Brain
Abstract
The project develops a formalism for bridging the gap between symbolic and dynamic levels of the mathematical theory of the brain. The formalism is based on the hypotheses that the neocortex processes symbolic information in a nonclassical way. Instead of manipulating data in a read/write memory, as the classical symbolic systems do, the neocortex changes the states of dynamic memory representing different temporary attributes of data stored in a long-term memory. This nonclassical symbolic/dynamic computational paradigm is called the concept of E-machine. Intuitively, an E-machine manipulates characteristic functions over the sets of memory addresses of data rather than addresses and data themselves. The main results include: (1) demonstrating the Turing universality of the E-machine paradigm, (2) showing how an E-machine can learn to simulate a read/write working memory without actually re-writing data, (3) demonstrating how the E-machine paradigm can be efficiently implemented in biologically-realistic neural networks with temporal modulation. Several computer simulations supporting the theoretical results were performed.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 27, 2009
- Accession Number
- ADA586715
Entities
People
- Victor Eliashberg
- Yakov Eliashberg