arXiv:2503. 18219v2 Announce Type: replace Abstract: This work studies the sampling complexity of learning with ReLU neural networks and neural operators.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2603. 00819v2 Announce Type: replace-cross Abstract: This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory.
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of 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: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:2606. 17419v1 Announce Type: new Abstract: We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms.
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.