22 citations · 25 across the 13 of their papers we have counts for
15 papers
Universal approximation of continuous maps between topological vector spaces
Emanuele Zappala
We study the problem of universal approximation of continuous maps between topological vector spaces by neural networks. We provide a universal approximation theorem for maps betwe…
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…
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…
Non-Markovian Discrete Diffusion with Causal Language Models
Yangtian Zhang, Sizhuang He, Daniel Levine +7
Discrete diffusion models offer a flexible, controllable approach to structured sequence generation, yet they still lag behind causal language models in expressive power. A key lim…
CaLMFlow: Volterra Flow Matching using Causal Language Models
Sizhuang He, Daniel Levine, Ivan Vrkic +6
We introduce CaLMFlow (Causal Language Models for Flow Matching), a novel framework that casts flow matching as a Volterra integral equation (VIE), leveraging the power of large la…
Intelligence at the Edge of Chaos
Shiyang Zhang, Aakash Patel, Syed A Rizvi +5
We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to pr…
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.…
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…
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…
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…
Operator Learning Meets Numerical Analysis: Improving Neural Networks through Iterative Methods
Emanuele Zappala, Daniel Levine, Sizhuang He +3
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing paral…
Continuous Spatiotemporal Transformers
Antonio H. de O. Fonseca, Emanuele Zappala, Josue Ortega Caro +1
Modeling spatiotemporal dynamical systems is a fundamental challenge in machine learning. Transformer models have been very successful in NLP and computer vision where they provide…
FIMP: Foundation Model-Informed Message Passing for Graph Neural Networks
Syed Asad Rizvi, Nazreen Pallikkavaliyaveetil, David Zhang +15
Foundation models have achieved remarkable success across many domains, relying on pretraining over vast amounts of data. Graph-structured data often lacks the same scale as unstru…
Neural Integral Equations
Emanuele Zappala, Antonio Henrique de Oliveira Fonseca, Josue Ortega Caro +4
Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challe…
Neural Integro-Differential Equations
Emanuele Zappala, Antonio Henrique de Oliveira Fonseca, Andrew Henry Moberly +4
Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that…