数字自带嵌入，无需训练即可保留加乘结构。
Numbers Already Carry Their Own Embeddings
- 基于数的实值与模运算特征构造嵌入，天然保持数学结构
- 在代数组合任务中实现首个完美准确率，如编织模式任务
- 无需重训练，可直接接入现有模型，适合需要数值推理的场景
我们提出无训练的阿德拉嵌入（AOE），该表示同时捕捉数字的实值及其模（p进）特征。该构造从设计上保持加法和乘法结构，将数值输入转化为“用数学语言说话”的嵌入。相比依赖特定任务重训练的先前方法，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，其表现持续提升，首次在编织模式任务上实现完美准确率，为解决人工智能长期存在的“数字难题”提供了原则性路径。
原文摘要 · Abstract (English)
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.
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