4 papers
Geometric instability of out of distribution data across autoencoder architecture
Susama Agarwala, Ben Dees, Corey Lowman
We study the map learned by a family of autoencoders trained on MNIST, and evaluated on ten different data sets created by the random selection of pixel values according to ten dif…
Eigenvalues of Autoencoders in Training and at Initialization
Benjamin Dees, Susama Agarwala, Corey Lowman
In this paper, we investigate the evolution of autoencoders near their initialization. In particular, we study the distribution of the eigenvalues of the Jacobian matrices of autoe…
Geometry and Generalization: Eigenvalues as predictors of where a network will fail to generalize
Susama Agarwala, Benjamin Dees, Andrew Gearhart +1
We study the deformation of the input space by a trained autoencoder via the Jacobians of the trained weight matrices. In doing so, we prove bounds for the mean squared errors for…
Rectifiability of the Singular Set of Harmonic Maps into Buildings
Ben Dees
We prove that the singular set of an energy-minimizing map from Euclidean space into an -connected complex is -rectifiable. This strengthens the regularity result of Grom…