Search Results for author:
Found 4 papers, 1 papers with code
Hidden symmetries of ReLU networks
The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation?
Functional dimension of feedforward ReLU neural networks
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 piecewise linear functions with finitely many pieces.
Local and global topological complexity measures OF ReLU neural network functions
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-connected feedforward ReLU neural network functions, F: R^n -> R. Along the way, we show how to construct, for each such F, a canonical polytopal complex K(F) and a deformation retract of the domain onto K(F), yielding a convenient compact model for performing calculations.
On transversality of bent hyperplane arrangements and the topological expressiveness of ReLU neural networks
We use this obstruction to prove that a decision region of a generic, transversal ReLU network F: R^n -> R with a single hidden layer of dimension (n + 1) can have no more than one bounded connected component.
