Simple mechanisms for representing, indexing and manipulating concepts

TL;DR — We introduce a simple sketch for defining concepts mathematically and building recursive structures out of these concepts.

Abstract

Deep networks typically learn concepts via classifiers, which involves setting up a model and training it via grading descent to fit the concept-labeled data. We will argue instead that learning a concept could be done by looking at its moment statistics matrix to generate a concrete representation or signature of that concept. These signatures can be used to discover structure across the set of concepts and could recursively produce higher-level concepts by learning this structure from those signatures. Concepts can be ’intersected’ to find a common theme in a number of related concepts. This process could be used to keep a dictionary of concepts so that inputs could correctly identify and be routed to the set of concepts involved in the (latent) generation of the input.