On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning
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Abstract (arXiv)
The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 17 of its 32 references that are in the map. First posted on arXiv 22 Dec 2025.
Builds on
17 of 32 references.
References · 17
- 2017Spectrally-normalized margin bounds for neural networkscited by 686
- 2015Norm-Based Capacity Control in Neural Networkscited by 299
- 2017Size-Independent Sample Complexity of Neural Networkscited by 290
- 2018Sensitivity and Generalization in Neural Networks: an Empirical Studycited by 189
- 2019Orthogonal Deep Neural Networkscited by 72
- 2019Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentationcited by 71
- 2019Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margincited by 56
- 2022Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guaranteescited by 34
- 2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
- 2023Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compressioncited by 18
- 2016Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learningcited by 16
- 2023Provable Multi-Task Representation Learning by Two-Layer ReLU Neural Networkscited by 16
5 more
- 2023Koopman-based generalization bound: New aspect for full-rank weightscited by 9
- 2024Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networkscited by 8
- 2022Fast Kernel Methods for Generic Lipschitz Losses via p-Sparsified Sketchescited by 5
- 2024Enhanced Feature Learning via Regularisation: Integrating Neural Networks and Kernel Methodscited by 5
- 2024Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learningcited by 2
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Citing papers per year: 2026: 1.
1 paper.