arXiv:2607.05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks. Functions in our spaces are defined recursively as $\ell^1$-bounded linear combinations of activated functions from preceding layers, with a dictionary of affine functions at the first layer. Unlike existing theories that are largely specialized to homogeneous activations such as the ReLU, our framework provides a meaningful notion of functional complexity for deep networks with a broad range of homogeneous and non-homogeneous activation functions commonly used
This research is emerging as the theoretical foundations of deep learning continue to be explored and refined, especially given the rapid practical advancements in AI. The increased complexity and diversity of neural network architectures necessitate more generalized theoretical frameworks.
A unifying theory for deep neural networks across various activation functions could unlock new design principles, improve interpretability, and lead to more robust and efficient AI models. This fundamental work contributes to the long-term maturation of AI as an engineering discipline.
The understanding of 'functional complexity' in deep networks may become more generalized, potentially enabling the development of new paradigms for designing and analyzing AI architectures beyond current specialized theories. This could broaden the scope of effective deep learning applications and deepen our theoretical grasp of their capabilities.
- · AI researchers
- · Deep learning framework developers
- · Academic institutions
- · Developers relying solely on ad-hoc deep learning design
Improved theoretical understanding of deep neural networks across diverse activation functions.
Potential for new, more efficient, and interpretable deep learning architectures based on this unified theory.
Accelerated innovation in AI applications by reducing the trial-and-error approach to network design and offering better performance predictability.
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Read at arXiv cs.LG