$p$-adic Manifold Learning and Benchmark Tasks from Impartial Games

Tomoki Mihara

cs.LGMay 6, 2026

$p$ -adic Manifold Learning and Benchmark Tasks from Impartial Games

Authors: Tomoki Mihara

Abstract

We introduce $p$ -adic manifold learning, propose an algorithm to solve it, and propose benchmark tasks from impartial games.

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Jun 12, 2026 · cs.LGJ/K move · Enter open · S save

Numbers Already Carry Their Own Embeddings

Suhyun Bae, Donghun Lee

Department of Mathematics Korea University

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.

Global Embeddings Combinations

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Abstract

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