The Geometry of Concept Learning
Understanding the neural basis of the remarkable human cognitive capacity to learn novel 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 that can be learnt from 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 readout neuron learns to discriminate new concepts based on few examples using a simple plasticity rule. We demonstrate the computational power of our 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 linguistic descriptors. 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 numerical simulations. We discuss testable predictions of our theory for psychophysics and neurophysiological experiments.