Talk page
Title:
Relations between numerical geometry and machine learning
Speaker:
Abstract:
This talk will start out with the formal parallel between machine learning and the numerical geometry methods discussed in several talks at this workshop. Essentially, the dataset for numerical geometry is a point cloud sampled from the manifold together with pointwise values of geometric quantities such as the Kahler potential or metric. Both ML and numerical geometry use general function approximators (neural networks) and optimize an accuracy measure (loss function). From this starting point, we go on to compare the theory on both sides. Much studied issues in ML include approximating power, non-convexity of the loss function and overparameterization. One usually takes a statistical viewpoint and studies generalization and robustness to errors.By contrast our geometric problems give rise to platonic datasets with simple definitions and universal properties. And in geometry we are interested in higher dimensional quantities (p-forms, simplicial complexes, gauge connections etc.) which are not unknown in ML but not well known either. We will explain the points of contact and suggest interesting possibilities for exchange of ideas.
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