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This construction preserves additive and multiplicative structure by design, turning 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 drops seamlessly into existing architectures. On algebraic combinatorics benchmarks, it delivers consistent gains including the first-ever perfect accuracy on the Weaving Pattern task-while suggesting a principled path forward for overcoming the long-standing \"number problem\" in AI.","title":"Numbers Already Carry Their Own Embeddings","url":"https://arxiv.org/abs/2606.14108","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.14108v1 Announce Type: cross \nAbstract: 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 structure by design, turning 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 drops seamlessly into existing architectures. 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