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math.NA2026
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…
math.NA2025
Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective
Simone Brivio, Nicola Rares Franco
Deep autoencoders have become a fundamental tool in various machine learning applications, ranging from dimensionality reduction and reduced order modeling of partial differential…
math.NA2024★ 1 cited
Measurability and continuity of parametric low-rank approximation in Hilbert spaces: linear operators and random variables
Nicola Rares Franco
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternativ…