75 citations · 135 across the 14 of their papers we have counts for
16 papers
On Functional Dimension and Persistent Pseudodimension
J. Elisenda Grigsby, Kathryn Lindsey
For any fixed feedforward ReLU neural network architecture, it is well-known that many different parameter settings can determine the same function. It is less well-known that the…
Functional dimension of feedforward ReLU neural networks
J. Elisenda Grigsby, Kathryn Lindsey, Robert Meyerhoff +1
It is well-known that the parameterized family of functions representable by fully-connected feedforward neural networks with ReLU activation function is precisely the class of pie…
Local and global topological complexity measures OF ReLU neural network functions
J. Elisenda Grigsby, Kathryn Lindsey, Marissa Masden
We apply a generalized piecewise-linear (PL) version of Morse theory due to Grunert-Kuhnel-Rote to define and study new local and global notions of topological complexity for fully…
On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks
J. Elisenda Grigsby, Kathryn Lindsey
Let F:R^n -> R be a feedforward ReLU neural network. It is well-known that for any choice of parameters, F is continuous and piecewise (affine) linear. We lay some foundations for…
An action of gl(1|1) on odd annular Khovanov homology
J. Elisenda Grigsby, Stephan M. Wehrli
We define an annular version of odd Khovanov homology and prove that it carries an action of the Lie superalgebra which is preserved under annular Reidemeister…
On braided, banded surfaces and ribbon obstructions
J. Elisenda Grigsby
We discuss how to apply work of L. Rudolph to braid conjugacy class invariants to obtain potentially effective obstructions to a slice knot being ribbon. We then apply these ideas…