In this paper, we introduce Adelic Operation-Preserved Embeddings (AOE), a training-free representation that captures both a number's real value and its modular (p-adic) signatures. This construction preserves additive and multiplicative structures by design, transforming numerical input into embeddings that 'speak in the language of mathematics.' Unlike prior approaches that rely on task-specific retraining, AOE is plug-and-play and seamlessly integrates into existing architectures.
On algebraic combinatorics benchmarks, AOE consistently delivers performance gains, including achieving the first-ever perfect accuracy on the Weaving Pattern task. This suggests a principled path forward for addressing the long-standing 'number problem' in AI.
Blogger's Review: The introduction of AOE marks a revolutionary advancement in the field of numerical representation, showcasing exceptional performance without the need for retraining. This embedding method not only improves computational efficiency but also offers new insights into solving complex issues in AI, making it worthy of attention and further research.