arXiv:2606. 14108v1 Announce Type: cross Abstract: 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.
arXiv:2609.39294v1 Announce Type: new Abstract: Precise numerical reasoning with Large Language Models (LLMs) is essential for expanding their applicability to complex real-world tasks. However, text...
arXiv:2608. 13129v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong results on mathematical reasoning benchmarks yet remain unreliable on elementary numerical tasks, including magnitude comparison, large-integer arithmetic, fractions, and scientific notation.
arXiv:2606. 01372v1 Announce Type: cross Abstract: Can neural networks learn abstract algebraic rules, or do they merely memorize training patterns?
arXiv:2609.25438v1 Announce Type: new Abstract: Diverse pretraining has been shown to be an effective method for learning reusable, domain-aware representations that provide a starting point for fine...
Large language models (LLMs) achieve strong results on mathematical reasoning benchmarks yet remain unreliable on elementary numerical tasks, including magnitude comparison, large-integer arithmetic, fractions, and scientific notation. This survey examines basic numerical understanding as a capability distinct from high-level mathematical reasoning.
arXiv:2606. 23044v2 Announce Type: replace-cross Abstract: Numbers have algebraic structure that standard neural embeddings often fail to expose.
arXiv:2606. 03645v1 Announce Type: cross Abstract: Large Language Models exhibit paradoxical fragility in fundamental arithmetic, implying a disconnect between internal computation and discrete output.
Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
arXiv:2505. 23851v2 Announce Type: replace-cross Abstract: Large language models (LLMs) are increasingly applied to symbolic mathematics, yet existing evaluations often conflate pattern memorization with genuine reasoning.
arXiv:2505. 23696v2 Announce Type: replace Abstract: Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields.
arXiv:2607. 07066v1 Announce Type: cross Abstract: Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition.
arXiv:2607. 09721v1 Announce Type: cross Abstract: To help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants.