Emergence of Object Representations in Brain Sensory Hierarchies
Humans and animals are able to recognize objects in high-dimensional sensory streams despite their sensitivity to low-level nuisance variables such as, orientation, pose, scale, location, and intensity. How neuronal systems perform the feat of invariant object classification and recognition is a fundamental problem in brain theory. Another impressive cognitive skill – also poorly understood – is the ability to learn to discriminate new objects or concepts based only on a few examples (a property known as few-shot learning).
The recent outstanding success of artificial deep neural networks in a variety of real-life visual processing tasks, including object recognition, calls for new ‘macroscopic’ theories of the neural representation of objects. I will present a recent statistical-mechanical theory based on the notion of object manifolds, i.e., the sets of all neuronal response vectors induced by different physical instantiations of single objects. The theory defines novel geometric measures – manifold radius and dimension – and establishes the relationship between these measures and high-level perceptual skills such as the capacity for classification of a large number of familiar objects, and the ability to perform few-shot learning of new objects.
I will show how this theory illuminates the principles underlying the transformation of object representations across layers of artificial deep neural networks. Electrical recordings from neurons at several stages of the visual cortex, responding to object and face stimuli, have been similarly analyzed, thereby shedding light on the correspondence between artificial deep networks and the visual hierarchy in the primate brain.
Overall, this work extends the reach of statistical mechanics to the neural information processing of high-dimensional data with rich, naturalistic statistical structures. Related problems at the interface between statistical mechanics, brain theory, and AI will be briefly discussed.