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.
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:2606. 01244v2 Announce Type: replace-cross Abstract: Inspired by the function-space theory of neural networks, we formulate and analyze a variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation.
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.
arXiv:2609.21422v1 Announce Type: cross Abstract: Deep representation learning often selects hidden features and fits the final predictor on the same sample, so fixed-feature analysis performed after...
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2608. 11661v1 Announce Type: cross Abstract: A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings.
arXiv:2606. 01244v1 Announce Type: cross Abstract: We study operator learning using encoder--decoder neural networks.
arXiv:2609. 21693v1 Announce Type: new Abstract: Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms.
arXiv:2609.15355v1 Announce Type: cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural network...
arXiv:2606. 15812v1 Announce Type: new Abstract: Constructing mathematically tractable function spaces that capture hierarchical compositional representations remains a central challenge in statistical learning theory.
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.