A framework for a theory of automated learning

Abstract

This paper describes a topological theory of learning which characterizes learning as a homotopy (which is a function of the deformation of a space in time) from an original knowledge base to one augmented by learned knowledge. The knowledge representation, the algorithms and the theory are based on the cognitive theories of Jean Piaget, the psychological theories of Hebb, as well as the ethological theories of Merzenich and Kaas. The choice of topology as a descriptive and predictive theory was inspired by the neurological aspects of synaptic routing under learning, which preserves the original continuity of the routes. Topology was chosen as a basis for a theory of learning as it is the study of space invariants which preserve the structure and continuity of a space under “stretchings and deformations”. Topology also offers a theoretical description of learning which does not revert to second-order logic. It has been shown that learning can be characterized by second-order logic, but any algorithm based on it is NP-complete.