The Geometry of Concept Learning

Understanding the neural basis of our remarkable cognitive capacity to accurately learn novel high-dimensional naturalistic concepts from just one or a few sensory experiences constitutes a fundamental problem. We propose a simple, biologically plausible, mathematically tractable, and computationally powerful neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts we can learn given few examples are defined by tightly circumscribed manifolds in the neural firing rate space of higher order sensory areas. We further posit that a single plastic downstream neuron can learn such concepts from few examples using a simple plasticity rule. We demonstrate the computational power of our simple proposal by showing it can achieve high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network models of these representations, and can even learn novel visual concepts specified only through language descriptions. Moreover, we develop a mathematical theory of few-shot learning that links neurophysiology to behavior by delineating several fundamental and measurable geometric properties of high-dimensional neural representations that can accurately predict the few-shot learning performance of naturalistic concepts across all our experiments. We discuss several implications of our theory for past and future studies in neuroscience, psychology and machine learning.