Hierarchical Kernel Machines: The Mathematics of Learning Inspired by Visual Cortex.

摘要

Understanding how the brain works and reproducing its central capabilities in computers is arguably one of the greatest problems in science and engineering. This project directly contributes to this challenge from both a mathematical and an applied point of view. In particular, we have developed a mathematical description of a family of hierarchical architectures for learning, comprised of a collection of definitions, lemmas and theorems which collectively highlight important and salient properties of such architectures. Most important among these properties is the notion of invariance. The theory we have developed characterizes how and why a hierarchical architecture can offer better generalization from few examples in terms capturing and exploiting symmetries in the physical world by way of learning invariances. A comprehensive suite of distributed, GPU-enabled software tools was developed to quickly test hypotheses and validate the theory on large-scale, real-world datasets.