Neurally-plausible radial basis kernels using distributed Fourier embeddings

TL;DR

This paper analyzes radial basis kernels within neurally plausible spatial representations, demonstrating their optimality and potential for coherent physical and perceptual modeling.

Contribution

It characterizes common radial basis kernels in a neurally plausible framework and shows grid cell-like representations are optimal for these kernels.

Findings

Radial basis kernels can be realized in spatial semantic pointer frameworks.

Grid cell-like representations are capable of implementing radial basis kernels.

Such representations are shown to be optimal for realizing these kernels.

Abstract

Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In this work, we aim to characterize and analyze common radial basis kernels realizable in the neurally-plausible framework of spatial semantic pointers. Further, we analyze previous radial basis kernel work based on grid cell-like representations and demonstrate that such representations are both capable of and optimal for realizing radial basis kernels.