Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.00642 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909630519574528 |
|---|---|
| author | Ji, Yuliang Wu, Jian Xi, Yuanzhe |
| author_facet | Ji, Yuliang Wu, Jian Xi, Yuanzhe |
| contents | Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite significant progress, there currently exists no universal neural-based method for approximating matrix inversion. This paper presents a theoretical analysis demonstrating the fundamental limitations of neural networks in developing a general matrix inversion model. We expand the class of Lipschitz functions to encompass a wider array of neural network models, thereby refining our theoretical approach. Moreover, we delineate specific conditions under which neural networks can effectively approximate matrix inverses. Our theoretical results are supported by experimental results from diverse matrix datasets, exploring the efficacy of neural networks in addressing the matrix inversion challenge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rethinking Neural-based Matrix Inversion: Why can't, and Where can Ji, Yuliang Wu, Jian Xi, Yuanzhe Machine Learning Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite significant progress, there currently exists no universal neural-based method for approximating matrix inversion. This paper presents a theoretical analysis demonstrating the fundamental limitations of neural networks in developing a general matrix inversion model. We expand the class of Lipschitz functions to encompass a wider array of neural network models, thereby refining our theoretical approach. Moreover, we delineate specific conditions under which neural networks can effectively approximate matrix inverses. Our theoretical results are supported by experimental results from diverse matrix datasets, exploring the efficacy of neural networks in addressing the matrix inversion challenge. |
| title | Rethinking Neural-based Matrix Inversion: Why can't, and Where can |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.00642 |