Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks
arXiv:2606.14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers. From this abstract perspective, we define representation costs for arbitrary parametric models and reveal their induced (native) function spaces. This unifies recent function-space views of data-fitting methods. We also prove that many natural results hold in this abstract setting, including representer theorems for parametric methods on their native spaces. The framework also rigorously connects param
The proliferation of complex AI models necessitates deeper theoretical understanding of their underlying mechanisms and limitations, driving foundational research in representation learning.
A robust theoretical framework for understanding representation costs in AI will enable more efficient model design, improved generalization, and better management of computational resources, impacting the entire AI development lifecycle.
This research provides a unifying mathematical foundation for analyzing diverse parametric data-fitting methods, offering a fresh perspective on how deep neural networks learn and represent information.
- · AI researchers
- · Deep learning practitioners
- · Compute infrastructure providers
- · AI model developers
- · Inefficient AI development
- · Ad-hoc model design approaches
Refined theoretical understanding leads to more predictable and performant AI models.
Improved efficiency in model design could reduce the computational burden of developing and deploying advanced AI systems.
These foundational insights might pave the way for entirely new AI architectures that are both more powerful and less resource-intensive.
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Read at arXiv cs.LG