Seminar on Computational Learning and Adaptation

Continuous Numeric Methods for Learning and Reasoning

John F. Sowa
VivoMind Intelligence

Communication, memory, learning, and reasoning depend on signs, but not all signs are symbolic. Using only presymbolic signs, animals from fish to apes learn and reason successfully in ways that far surpass the abilities of systems that use the symbolic methods of artificial intelligence. Although the discrete symbols of language and logic are efficient for expressing information, the older mechanisms for integrating continuous geometric information from visual and tactile sources handle much larger amounts of information with more powerful computational mechanisms than current AI technology. This talk presents ongoing research on methods for bridging the gap between discrete language-like representations and continuous geometrical models, including (a) methods for encoding discrete knowledge representations in continuous knowledge signatures and (b) methods for processing knowledge signatures by a network of spreading computations, which are promising candidates for both a neurodynamic hypothesis and efficient computational methods. With this approach, numerical methods can be applied to traditional AI problems that require intractable exponential or polynomial algorithms that do not scale to large volumes of data. Continuous methods, by themselves, cannot make intractable problems tractable, but they can derive approximate solutions to certain problems which can then be verified by discrete methods. As an example, list-processing algorithms for analogy finding take N-cubed time, but algorithms based on knowledge signatures take only (N log N) time. The techniques can also be applied to the logic-based methods of induction, deduction, and abduction. The continuous methods do not replace all symbolic computation, but they speed up the most time-consuming part: indexing and finding relevant knowledge.

This talk reports work done jointly with Arun K. Majumdar, also at VivoMind. For more information, see:
John F. Sowa & Arun K. Majumdar (2003). Analogical reasoning. In A. de Moor, W. Lex, & B. Ganter (Eds.), Conceptual Structures for Knowledge Creation and Communication, LNAI 2746, Springer-Verlag, Berlin, pp. 16-36.
http://www.jfsowa.com/pubs/analog.htm

Return to the seminar schedule