8 papers
A short tour of operator learning theory: Convergence rates, statistical limits, and open questions
Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical…
Approximating Matrix Functions with Deep Neural Networks and Transformers
Rahul Padmanabhan, Simone Brugiapaglia
Transformers have revolutionized natural language processing, but their use for numerical computation has received less attention. We study the approximation of matrix functions, w…
On Continuous Terminal Embeddings of Sets of Positive Reach
Simone Brugiapaglia, Rafael Chiclana, Tim Hoheisel +1
In this paper we prove the existence of Hölder continuous terminal embeddings of any desired into with $m=\mathcal{O}(\varepsilon^{-2}ω(…
Provable Emergence of Deep Neural Collapse and Low-Rank Bias in -Regularized Nonlinear Networks
Emanuele Zangrando, Piero Deidda, Simone Brugiapaglia +2
We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained wit…
Model-adapted Fourier sampling for generative compressed sensing
Aaron Berk, Simone Brugiapaglia, Yaniv Plan +3
We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown t…
Square Root LASSO: Well-posedness, Lipschitz stability and the tuning trade off
Aaron Berk, Simone Brugiapaglia, Tim Hoheisel
This paper studies well-posedness and parameter sensitivity of the Square Root LASSO (SR-LASSO), an optimization model for recovering sparse solutions to linear inverse problems in…
LASSO reloaded: a variational analysis perspective with applications to compressed sensing
Aaron Berk, Simone Brugiapaglia, Tim Hoheisel
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In pa…
Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs
Simone Brugiapaglia, Sjoerd Dirksen, Hans Christian Jung +1
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance struct…