Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912973708066816 |
|---|---|
| author | Zhao, Hongjue Chen, Yizhuo Wang, Yuchen Qi, Hairong Sha, Lui Abdelzaher, Tarek Shao, Huajie |
| author_facet | Zhao, Hongjue Chen, Yizhuo Wang, Yuchen Qi, Hairong Sha, Lui Abdelzaher, Tarek Shao, Huajie |
| contents | Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a theoretical foundation for understanding, analyzing, and improving DNNs. We organize the discussion around three guiding questions: i) how differential equations offer a principled understanding of DNN architectures, ii) how tools from differential equations can be used to improve DNN performance in a principled way, and iii) what real-world applications benefit from grounding DNNs in differential equations. We adopt a two-fold perspective spanning the model level, which interprets the whole DNN as a differential equation, and the layer level, which models individual DNN components as differential equations. From these two perspectives, we review how this framework connects model design, theoretical analysis, and performance improvement. We further discuss real-world applications, as well as key challenges and opportunities for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18331 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations Zhao, Hongjue Chen, Yizhuo Wang, Yuchen Qi, Hairong Sha, Lui Abdelzaher, Tarek Shao, Huajie Artificial Intelligence Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a theoretical foundation for understanding, analyzing, and improving DNNs. We organize the discussion around three guiding questions: i) how differential equations offer a principled understanding of DNN architectures, ii) how tools from differential equations can be used to improve DNN performance in a principled way, and iii) what real-world applications benefit from grounding DNNs in differential equations. We adopt a two-fold perspective spanning the model level, which interprets the whole DNN as a differential equation, and the layer level, which models individual DNN components as differential equations. From these two perspectives, we review how this framework connects model design, theoretical analysis, and performance improvement. We further discuss real-world applications, as well as key challenges and opportunities for future research. |
| title | Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2603.18331 |