13 papers
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…
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…
Formulating Beurling LASSO for Source Separation via Proximal Gradient Iteration
Sören Schulze, Emily J. King
Beurling LASSO generalizes the LASSO problem to finite Radon measures regularized via their total variation. Despite its theoretical appeal, this space is hard to parametrize, whic…
Blind Source Separation in Polyphonic Music Recordings Using Deep Neural Networks Trained via Policy Gradients
Sören Schulze, Johannes Leuschner, Emily J. King
We propose a method for the blind separation of sounds of musical instruments in audio signals. We describe the individual tones via a parametric model, training a dictionary to ca…
A note on tight projective 2-designs
Joseph W. Iverson, Emily J. King, Dustin G. Mixon
We study tight projective 2-designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2-design in every dimensio…
Nonclosedness of Sets of Neural Networks in Sobolev Spaces
Scott Mahan, Emily King, Alex Cloninger
We examine the closedness of sets of realized neural networks of a fixed architecture in Sobolev spaces. For an exactly -times differentiable activation function , we constru…