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.

翻译：我们提出Adelic运算保持嵌入（AOE），这是一种无需训练的表示方法，既能捕捉数字的实数值，也能捕捉其模（p-adic）特征。该构造通过设计保留了加法和乘法结构，将数值输入转化为“用数学语言表达”的嵌入。不同于依赖特定任务重新训练的现有方法，AOE即插即用，可无缝集成到现有架构中。在代数组合基准测试中，它取得了持续性的性能提升，包括在编织模式任务上首次实现完美准确率——同时为克服AI中长期存在的“数字问题”提供了原则性路径。