Location, Location, Location: Design Bias with Kernel Transformation

Xin Li

Keywords: implicit representation; concentration of measure; recursive kernel transformation; design bias; manifold learning

TL;DR: Location, Location, Location

Abstract: It has been hypothesized that the old brain was compressed into cortical columns of the neocortex during the evolution of mammalian brains. Computational modeling of hippocampal-cortical interaction inspires us to propose a navigation-based implicit representation for manifold learning. The key new insight is to transform any explicit function (or geometrically a manifold) to an implicit representation using design bias for exploiting the concentration of measure (CoM) in high dimensional spaces. CoM-based blessing of dimensionality enables us to solve the manifold learning problem by direct-fit or local computation with guaranteed generalization property and without the need to discover global topology. We construct a memory encoding model, namely specification-before-generalization (SbG), and extend it into recursive kernel transformation to mirror the nested structure of the physical world. The biological plausibility of SbG learning is supported by its consistency with the wake-sleep cycles of mammalian brains. Finally, we showcase the application of design bias and recursive kernel transformation to understanding the phylogenetic continuity of navigation and memory and the manifold untangling of object recognition by the ventral stream.

Primary Area: learning theory

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Submission Number: 1950