4 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…
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}υ
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…
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…