172 citations · 305 across the 36 of their papers we have counts for
40 papers
Trefoil Probabilities and Polyhedra
Joseph Geisz, Chris Peterson, Clayton Shonkwiler
We determine the exact probability that the closed hexagonal polygon obtained by cyclically joining six independent points uniformly distributed on the unit sphere is knotted. The…
ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog
Yajing Liu, Christina M Cole, Chris Peterson +1
A ReLU neural network leads to a finite polyhedral decomposition of input space and a corresponding finite dual graph. We show that while this dual graph is a coarse quantization o…
Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks
Huma Jamil, Yajing Liu, Christina M. Cole +4
Previous work has shown that a neural network with the rectified linear unit (ReLU) activation function leads to a convex polyhedral decomposition of the input space. These decompo…
Quasi-polynomial growth of numerical and affine semigroups with constrained gaps
Michael DiPasquale, Bryan R. Gillespie, Chris Peterson
A common tool in the theory of numerical semigroups is to interpret a desired class of semigroups as the integer lattice points in a rational polyhedron in order to leverage comput…
The Flag Median and FlagIRLS
Nathan Mankovich, Emily King, Chris Peterson +1
Finding prototypes (e.g., mean and median) for a dataset is central to a number of common machine learning algorithms. Subspaces have been shown to provide useful, robust represent…
Locally Linear Attributes of ReLU Neural Networks
Ben Sattelberg, Renzo Cavalieri, Michael Kirby +2
A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the inp…