On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916060057305088 |
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| author | Mohammadigohari, Mahdi Di Fatta, Giuseppe Nicosia, Giuseppe Pardalos, Panos M. |
| author_facet | Mohammadigohari, Mahdi Di Fatta, Giuseppe Nicosia, Giuseppe Pardalos, Panos M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning Mohammadigohari, Mahdi Di Fatta, Giuseppe Nicosia, Giuseppe Pardalos, Panos M. Machine Learning Artificial Intelligence 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. |
| title | On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2512.19199 |