Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation
arXiv:2606.26705v1 Announce Type: new Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes. While powerful, this perspective is incomplete: it primarily captures complexity through regularity, and therefore does not distinguish intuitively simple and complicated objects with comparable regularity, such as the square-root function and a typical Brownian path. The guiding message is that neural networks should be viewed not only as flexible basis functions, but also as models of computation. If a function is computable by a real
This paper offers a new theoretical framework for understanding deep learning expressivity, shifting focus from regularity to computability, reflecting ongoing basic research in AI foundations.
A strategic reader should care because deeper theoretical understanding of neural networks can unlock new design principles, leading to more efficient, powerful, or specialized AI architectures.
The theoretical lens through which neural network capabilities are analyzed changes, potentially impacting future architectural choices and the types of problems deemed tractable or efficient for AI.
- · AI researchers
- · Deep learning framework developers
- · Specialized AI applications
- · Heuristic-driven AI development
- · Purely empirical AI optimization
- · Those reliant on current architectural assumptions
This research provides a more robust theoretical foundation for why certain neural network architectures perform effectively.
Improved theoretical understanding could guide the development of novel AI models that are a step-change in efficiency or capability for specific tasks.
These foundational insights might eventually inform the creation of new AI paradigms beyond current deep learning, profoundly impacting future technological landscapes.
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Read at arXiv cs.LG