8 papers
Projection Methods for Operator Learning and Universal Approximation
Emanuele Zappala
We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping. Moreover, we introduce an…
Neural Integral Operators for Inverse Problems: An Operator-Learning Framework for Small-Sample Spectroscopic Classification
Emanuele Zappala, Alice Giola, Andreas Kramer +2
Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architecture…
Nonlocal operator learning for fMRI encoding and decoding tasks
Andreas Kramer, Saugat Acharya, Alice Giola +1
Functional MRI data exhibit high-dimensional spatiotemporal structure, making both prediction and decoding challenging. In this work, we investigate neural integral-operator-based…
Universal Approximation of Operators with Transformers and Neural Integral Operators
Emanuele Zappala, Maryam Bagherian
We study the universal approximation properties of transformers and neural integral operators for operators in Banach spaces. In particular, we show that the transformer architectu…
Leray-Schauder Mappings for Operator Learning
Emanuele Zappala
We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces.…
Spectral methods for Neural Integral Equations
Emanuele Zappala
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of th…