arXiv:2402.00094v3 Announce Type: replace-cross Abstract: We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of r
This research, published in 2026, represents a theoretical advancement in deep neural network architecture, building on foundational mathematical concepts.
It introduces a novel mathematical framework for designing robust and universal deep neural networks, potentially leading to more efficient and powerful AI models.
The theoretical underpinnings of DNN design could expand to include non-Archimedean analysis, offering new avenues for developing advanced AI capabilities.
- · AI researchers
- · Machine learning developers
- · Mathematical AI startups
New theoretical foundations for AI model design emerge.
This could lead to a new generation of more robust and universal AI algorithms.
Advanced AI models with improved performance across various tasks become more accessible, driving further AI integration.
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Read at arXiv cs.AI