arXiv Machine Learning
Jun 2
Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces
arXiv:2606. 01244v1 Announce Type: cross Abstract: We study operator learning using encoder--decoder neural networks.
New universal operator approximation theorem for encoder-decoder architectures
arXiv:2503. 24092v2 Announce Type: replace-cross Abstract: Motivated by the rapidly growing field of mathematics for operator approximation with neural networks, we present a novel universal operator approximation theorem for broad classes of encoder-decoder architectures and a wide range of input and output spaces.
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arXiv AI
Jul 13
Projection Methods for Operator Learning and Universal Approximation
arXiv:2406. 12264v5 Announce Type: replace-cross Abstract: We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping.
arXiv Machine Learning
Jun 16
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
arXiv:2606. 16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks.
arXiv Machine Learning
Aug 10
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.
arXiv Machine Learning
Jun 25
Structured Approximations of Measures
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
arXiv Machine Learning
1d ago
Operator-Theoretic Generalization Bounds for Multitask Deep Learning
arXiv:2608. 15982v1 Announce Type: new Abstract: We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces.
arXiv Machine Learning
Jun 16
Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks
arXiv:2606. 14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers.
arXiv Machine Learning
Jun 9
Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
arXiv:2606. 09820v1 Announce Type: cross Abstract: We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives.
Hugging Face Trending Papers
3d ago
Operator-Theoretic Generalization Bounds for Multitask Deep Learning
We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures.
arXiv AI
Jun 10
Mixtures of Neural Operators Reduce Active Complexity in Operator Learning
arXiv:2404. 09101v3 Announce Type: replace-cross Abstract: Operator-learning systems are not governed solely by total parameter count; for one query, the relevant bottleneck can be the model that must be loaded and evaluated.
arXiv Machine Learning
Aug 6
Discretization and Statistical Consistency of Functional Flow Matching
arXiv:2608. 04531v1 Announce Type: new Abstract: Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values.
arXiv Machine Learning
Jul 27
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
arXiv:2509. 26371v3 Announce Type: replace-cross Abstract: Recently, there has been growing interest in characterizing the function spaces underlying neural networks.