3 citations · 10 across the 6 of their papers we have counts for
9 papers
Topological Parallax: A Geometric Specification for Deep Perception Models
Abraham D. Smith, Michael J. Catanzaro, Gabrielle Angeloro +2
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…
Persistent Obstruction Theory for a Model Category of Measures with Applications to Data Merging
Abraham D. Smith, Paul Bendich, John Harer
Collections of measures on compact metric spaces form a model category ("data complexes"), whose morphisms are marginalization integrals. The fibrant objects in this category repre…
Geometric Cross-Modal Comparison of Heterogeneous Sensor Data
Christopher J. Tralie, Abraham Smith, Nathan Borggren +4
In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: ful…
Supervised Learning of Labeled Pointcloud Differences via Cover-Tree Entropy Reduction
Abraham Smith, Paul Bendich, John Harer +2
We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties…
Involutive Tableaux, Characteristic Varieties, and Rank-one Varieties in the Geometric Study of PDEs
Abraham D. Smith
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems…
Constructing Involutive Tableaux with Guillemin Normal Form
Abraham D. Smith
Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-Kähler…