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Banbury Center Workshop Series

Neurocomputational Strategies: From Synapses to Behavior (1998)
Functional Organization of the Thalamus and Cortex and their Interactions (1999)
Toward Animal Models of Attention and Consciousness (2000)
Persistent Neural Activity (2000)
Can a Machine Be Conscious? (2001)
Communication in Brain Systems (2004)
Neurobiology of Decision-Making (2005)
Computational Approaches to Cortical Functions (2006)
New Frontiers in Studies of Nonconscious Processing (2007)
Theoretical and Experimental Approaches to Auditory and Visual Attention (2008)
Searching for Principles Underlying Memory in Biological Systems (2009)
Neuronal Response Variability and Cortical Computation (2011)
Connections and Communication in the Brain (2014)

Tony Bell

Geometric and Dynamical Perspectives on ICA

Salk Institute

I will discuss ICA (or more generally, density estimation algorithms) from the point of view of Riemannian geometry. In particular, learning is viewed as a process of dynamically adjusting a non-linear metric tensor. This leads to the `Metric Ansatz': change the metric till the data looks uniformly distributed. As an example I will show the self-organisation from natural images of "complex cells": shift-invariant receptive fields. This is explained in terms of a shift from a L(1) to a L(2) norm, which corresponds to the discovery, by the learning system, of rotational symmetries in the natural scene statistics.