Numbers Already Carry Their Own Embeddings
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Computer Science > Machine Learning
Title:Numbers Already Carry Their Own Embeddings
Abstract: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. 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.
| Comments: | Presented at the MATH-AI Workshop at NeurIPS 2025 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.14108 [cs.LG] |
| (or arXiv:2606.14108v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.14108
arXiv-issued DOI via DataCite (pending registration)
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