Chad Giusti - Topology, Convexity, and Neural Networks

Explore the intersection of topology, convexity, and neural networks in this 45-minute lecture by Chad Giusti, presented as part of the Hausdorff Trimester Program on Applied and Computational Algebraic Topology. Delve into topics such as receptive fields, neuron convexity, and cofiring events, while examining the Nobel Prize-winning research on brain topology. Investigate the concept of inverse questions and geometric features in neural networks, and learn about open and dark convex structures. Discover the nerve theorem and its applications to feedforward neural networks, and consider the potential implications of convex codes in understanding brain function. Gain insights into cutting-edge research that bridges mathematical concepts with neuroscience, offering a unique perspective on the complexities of neural information processing.

Intro
Nobel Prize for Medicine
Receptive field
Topology
Topology in the brain
Receptive fields
Neuron convexity
John Oakey splice cells
Simpler picture
Cofiring events
Is it possible
Inverse question
Geometric features
Objective study
Open convex
Dark convex
Nerve theorem
Feedforward neural networks
Conjecture
Useful convex codes