46 citations · 70 across the 9 of their papers we have counts for
12 papers
Convergence of gradient flow for learning convolutional neural networks
Jona-Maria Diederen, Holger Rauhut, Ulrich Terstiege
Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This m…
Convergence of gradient descent for learning linear neural networks
Gabin Maxime Nguegnang, Holger Rauhut, Ulrich Terstiege
We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related…
Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers
Bubacarr Bah, Holger Rauhut, Ulrich Terstiege +1
We study the convergence of gradient flows related to learning deep linear neural networks (where the activation function is the identity map) from data. In this case, the composit…
Low-rank matrix recovery via rank one tight frame measurements
Holger Rauhut, Ulrich Terstiege
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval probl…
Stable low-rank matrix recovery via null space properties
Maryia Kabanava, Richard Kueng, Holger Rauhut +1
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery re…
Low rank matrix recovery from rank one measurements
Richard Kueng, Holger Rauhut, Ulrich Terstiege
We study the recovery of Hermitian low rank matrices from undersampled measurements via nuclear norm minimization. We consider the particular scenar…
The supersingular locus of the Shimura variety for GU(1,n-1) over a ramified prime
Michael Rapoport, Ulrich Terstiege, Sean Wilson
We analyze the geometry of the supersingular locus of the reduction modulo p of a Shimura variety associated to a unitary similitude group GU(1,n-1) over Q, in the case that p is r…
On the regularity of special difference divisors
Ulrich Terstiege
In this note we prove that the difference divisors associated with special cycles on unitary Rapoport-Zink spaces of signature (1,n-1) in the unramified case are always regular.
On the Arithmetic Fundamental Lemma in the minuscule case
Michael Rapoport, Ulrich Terstiege, Wei Zhang
The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli s…
Intersections of special cycles on the Shimura variety for GU(1,2)
Ulrich Terstiege
We establish a close connection between intersection multiplicities of special cycles on arithmetic models of the Shimura variety for GU(1,2) and Fourier coefficients of derivative…
Intersections of arithmetic Hirzebruch-Zagier cycles
Ulrich Terstiege
We establish a close connection between the intersection multiplicity of three arithmetic Hirzebruch-Zagier cycles and the Fourier coefficients of the derivative of a certain Siege…
Antispecial cycles on the Drinfeld upper half plane and degenerate Hirzebruch-Zagier cycles
Ulrich Terstiege
We define the notion of antispecial cycles on the Drinfeld upper half plane in analogy to the notion of special cycles defined by Kudla and Rapoport in their Inventiones paper. We…