arXiv:2510.09685v2 Announce Type: replace Abstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to theoretical understanding, interpretability, and generalization. To address these issues, researchers are increasingly adopting a differential equations perspective to propose a unified theoretical framework and systematic design methodologies for neural networks. In this paper, we provide an extensive review of
The explosion of deep learning applications has brought to the forefront persistent issues with interpretability and generalization, leading researchers to actively seek more robust theoretical foundations.
A deeper theoretical understanding of neural networks, informed by differential equations, promises to unlock greater reliability, efficiency, and broader applicability of AI systems across critical sectors.
Approaches to designing and training neural networks could fundamentally shift towards more structured, principled methodologies, moving away from purely empirical optimization.
- · AI researchers and academics
- · Companies developing AI for high-stakes applications (e.g., scientific computing
- · Hardware manufacturers optimizing for differentiable programming paradigms
- · Sectors requiring explainable AI
- · Organizations relying solely on black-box AI models
- · Empirical-only AI development methodologies
Improved interpretability and generalization capabilities of AI models.
Accelerated development of AI for scientific discovery and complex system control.
New AI architectures that are provably reliable under various conditions, impacting regulatory frameworks and societal trust.
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