# Numbers Already Carry Their Own Embeddings

arXiv: https://arxiv.org/abs/2606.14108 · HTML: https://mlsanity.com/paper/2606.14108/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 8 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics](https://mlsanity.com/paper/2503.06366/) (2025)

## Built on by (most cited first, 1 of 1)

- [Prime Fourier Embeddings: A Principled Basis for Modular Arithmetic](https://mlsanity.com/paper/2606.23044/) (2026)

## Abstract (arXiv)

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.