Numbers Already Carry Their Own Embeddings
For AI researchers working on numerical reasoning, this provides a plug-and-play embedding that preserves mathematical structure without task-specific retraining.
The paper introduces Adelic operation-preserved embeddings (AOE), a training-free representation that captures both real and modular number signatures, achieving the first perfect accuracy on the Weaving Pattern task and consistent gains on algebraic combinatorics benchmarks.
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.