Vector Symbolic Architectures: Analog computation on discrete data structures

Dr Ross Gayler (Veda Pty. Ltd. & LaTrobe University)

Historically, analog computation had advantages over digital computation in speed and parallelism. Computational problems were cast as dynamical systems, which was relatively straightforward for models of physical problems such as flight dynamics. However, it was far less clear how to translate computations on discrete data structures such as trees and graphs into dynamical systems. This is especially true for problems where the data structures evolve over time, implying the need to rewire the analog computer on the fly. This is relevant to cognitive science because neural network operation maps naturally to analog computation and cognitive tasks imply combinatorial, discrete data structures.

In this talk I describe Vector Symbolic Architectures, a family of mathematical techniques for analog computation in hyperdimensional vector spaces. VSAs naturally support computation on discrete data structures and a form of virtualisation that breaks the nexus between the items to be represented and the hardware that supports the representation. This means that computations on evolving data structures do not require physical rewiring of the implementing hardware. I illustrate this approach with a VSA system that finds isomorphisms between graphs and where different problems to be solved are represented by different initial states of the fixed hardware.
BIO:
Ross took an initial degree in computer science and psychology in an attempt to do cognitive science before it existed as a discipline. He went on to do a doctorate in experimental psychology (rats and stats minus the rats) which, somewhat unexpectedly, was a good grounding for a career in the statistical modelling of consumer credit behaviour. Ross has worked in the consumer credit industry since 1989 and continues to pursue cognitive science research in his spare time.