arXiv:2607.06781v1 Announce Type: new Abstract: In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error. We resolve this issue by introducing the Chinese Remainder Theorem as a constructive encoding mechanism. For Lipschitz continuous functions on $[0,1]^D$, we construct a width-$\max\{D,4\}$, depth-$5$
This research provides a concrete, non-asymptotic characterization of neural network approximation, addressing a gap in previous theoretical work on super-expressive networks.
Improved theoretical understanding of neural network expressivity, particularly with explicit parameter bounds, can lead to more efficient and reliable AI model design and deployment.
The ability to construct small, fixed-architecture neural networks with guaranteed approximation capabilities, avoiding the need for excessively large or complex models, is enhanced.
- · AI researchers
- · Machine learning engineers
- · AI hardware developers
- · Developers relying on heuristic model sizing
- · Companies with inefficient large models
This work directly improves the theoretical foundations for designing compact yet powerful neural networks.
It could enable the development of more resource-efficient AI models, applicable in edge computing and constrained environments.
This might accelerate the broader adoption of AI by making its computational demands more predictable and manageable.
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Read at arXiv cs.LG