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Paul Bendich

2 accepted papers

2023

Topological Parallax: A Geometric Specification for Deep Perception Models

NeurIPS 2023spotlight

For safety and robustness of AI systems, we introduce _topological parallax_ as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs and examples show that this geometric similar…

2021

A Fast and Robust Method for Global Topological Functional Optimization

AISTATS 2021poster

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable, allowing for topological gradients to be backpropagated to o…