Numbers Already Carry Their Own Embeddings

The article introduces Adelic operation-preserved embeddings (AOE), a novel training-free representation that captures both real values and modular signatures of numbers while preserving their additive and multiplicative structures. AOE integrates easily into existing architectures without the need for retraining and achieves significant performance improvements, including perfect accuracy on the Weaving Pattern task in algebraic combinatorics benchmarks. This advancement addresses the "number problem" in AI, offering a promising solution for practitioners working with numerical data in LLMs and AI applications.