Wednesday 4th October 2017
Ground Floor Seminar Room
25 Howland Street, London, W1T 4JG
Neural Processing of Object Manifolds
Objects are represented in each stage of the sensory hierarchy as manifolds due to variabilities in stimulus features such as location, orientation, and intensity. What makes manifold representations at higher stages of the hierarchy better suited for invariant decoding of object information by downstream circuits than earlier stages? It has been suggested that the sensory hierarchy becomes increasingly untangled, but the notion of “tangled manifolds” remains vague. In this work, we consider linear readout of objects as a model of biologically plausible computation of sensory signals to determine which statistical features of the neuronal representation of object manifolds are more amenable to this computation.
Extending the statistical mechanics of linear classification of random points, we establish a theory of linear classification of generic manifolds synthesizing statistical and geometric properties of high dimensional signals. The exact capacity of manifold classification generally depends on the full geometrical details of their convex hulls; however, we show that in a broad parameter regime, manifold classification depends primarily on two quantities: their effective dimension and their effective radius. We have developed a novel efficient algorithm that can learn the synaptic weights of the neuronal readout guaranteed to converge to the solution with good generalization and robustness properties. We demonstrate results from applying our method to both neuronal networks and deep networks from machine learning.