arXiv:2606.20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved. This paper studies the opposite possibility: can the network be chosen once and for all, and can accuracy be bought only by letting it run longer? We prove that this is possible for every continuous function on [-1,1]. More precisely, each such function is uniformly approximated by the time evolution of a single ReLU recurrent neural network with fixed weights and fixed hidden dimension. The mechanism behind the construction is a new intermedia
This foundational research arrives as the practical applications of AI are expanding rapidly, pushing the boundaries of what fixed AI architectures can achieve, and driving exploration into more dynamic and efficient learning paradigms.
A strategic reader should care because this research suggests a potential pathway to significantly more efficient and adaptable AI systems, allowing a single neural network to dynamically improve accuracy without needing retraining or architecture changes.
The paradigm shifts from needing new or retrained neural networks for improved accuracy to potentially using a single, fixed-weight recurrent neural network that improves merely by running for longer or with more iterations.
- · AI compute efficiency
- · AI software developers
- · Robotics and embedded AI
- · Traditional neural network retraining paradigms
- · High-energy AI model iteration
- · Certain specialized hardware requiring bespoke network designs
This research provides a new theoretical understanding of how recurrent neural networks can approximate continuous functions with fixed parameters.
It could lead to the development of more resource-efficient and continuously adaptive AI models that learn over time without requiring redeployment or re-compilation.
Such adaptive, fixed-architecture AI could enable the deployment of highly flexible autonomous agents in environments with limited compute, potentially accelerating progress in areas like humanoid robotics and constrained edge AI.
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Read at arXiv cs.LG