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15 papers in the last four weeks, up 67% on the four weeks before. 0.1% of all new papers.

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Which Spaces can be Embedded in $L_p$ -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
Oct 14, 2024Yiping Lu, Daozhe Lin, Qiang DuReproducing Kernel Hilbert Spaces Learnability
Industrial Engineering & Management Sciences, Northwestern University · Department of Applied Physics & Applied Mathematics, Columbia University
How Learning Dynamics Drive Adversarially Robust Generalization?
Oct 10, 2024Yuelin Xu, Xiao ZhangAdversarial Training Generalization Bounds
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Probabilistic Truly Unordered Rule Sets
Jan 18, 2024Lincen Yang, Matthijs van LeeuwenProbabilistic Model Learnability
LIACS, Leiden University Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands
Understanding Certified Training with Interval Bound Propagation
Jun 17, 2023Yuhao Mao, Mark Niklas Müller, Marc Fischer +1Neural Network Verification Learnability
Department of Computer Science, ETH Zürich, Swizterland
Reliable learning in challenging environments
Apr 6, 2023Maria-Florina Balcan, Steve Hanneke, Rattana Pukdee +1Learnability Provable Guarantees
Carnegie Mellon University · Purdue University
Limits of Transfer Learning
Jun 23, 2020Jake Williams, Abel Tadesse, Tyler Sam +2Transfer Learning Learnability
Harvey Mudd College, Claremont, CA 91711, USA · Claremont McKenna College, Claremont, CA 91711, USA · Pomona College, Claremont, CA 91711, USA

Oct 14, 2024, math.NAJ/K move · Enter open · S save

Which Spaces can be Embedded in $L_p$ -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy

Yiping Lu, Daozhe Lin, Qiang Du

Industrial Engineering & Management Sciences, Northwestern University · Department of Applied Physics & Applied Mathematics, Columbia University

Reproducing Kernel Hilbert Spaces Learnability Approximation Algorithms

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In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function spaces and has implications for their approximability and learnability. Classical results show that embedding a function space into a reproducing kernel Hilbert space (RKHS) implies a bound on its metric entropy growth. Surprisingly, we prove a \textbf{converse}: a bound on the metric entropy growth of a function space allows its embedding to a

L_p-

type Reproducing Kernel Banach Space (RKBS). This shows that the

{L}_p-

type RKBS provides a broad modeling framework for learnable function classes with controlled metric entropies. Our results shed new light on the power and limitations of kernel methods for learning complex function spaces.

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Latest papers 126

Which Spaces can be Embedded in LpL_pLp​-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy

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Reliable learning in challenging environments

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Which Spaces can be Embedded in $L_p$ -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy