1 citations · 1 across the 4 of their papers we have counts for
8 papers
Separation Capacity of Scattering Networks on Low-Dimensional Datasets
Konstantin Häberle, Helmut Bölcskei
We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial non…
Function-Counting Theory for Low-Dimensional Data Structures
Konstantin Häberle, Helmut Bölcskei
The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-…
Matrix Discrepancy for Representations of Finite Groups
Afonso S. Bandeira, Helmut Bölcskei
We prove the group version of the Matrix Spencer conjecture. For every finite group , there exist signs such that $$\left\| \sum_{g\in G} \varepsilon_…
Metric Entropy of Analytic Function Classes via Ellipsoidal Methods
Thomas Allard, Helmut Bölcskei
We present a systematic methodology for characterizing the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. The approach does not rely on th…
Entropy and Minimax Risk of Hypoelliptic Pseudodifferential Operators
Thomas Allard, Helmut Bölcskei
We characterize the entropy and minimax risk of a broad class of compact pseudodifferential operators. Under suitable decay and regularity conditions on the symbol, we combine a We…
Metric Entropy of Ellipsoids in Banach Spaces: Techniques and Precise Asymptotics
Thomas Allard, Helmut Bölcskei
We develop new techniques for computing the metric entropy of ellipsoids -- with polynomially decaying semi-axes -- in Banach spaces. Besides leading to a unified and comprehensive…