# Attention-Graph Curvature for the Verification of Mathematical Reasoning

arXiv: https://arxiv.org/abs/2610.16709 · HTML: https://mlsanity.com/paper/2610.16709/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 6 of 6)

- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature](https://mlsanity.com/paper/2211.15779/) (2022)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [ReProbe: Efficient Test-Time Scaling of Multi-Step Reasoning by Probing Internal States of Large Language Models](https://mlsanity.com/paper/2511.06209/) (2025)
- [Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning](https://mlsanity.com/paper/2601.00791/) (2026)

## Abstract (arXiv)

Language models have recently solved open ErdHos problems and achieved gold-medal level performance on International Mathematical Olympiad problems. But their solutions, written in natural language, cannot yet be verified by proof assistants. An erroneous reasoning step can invalidate every step that comes after, so it is advantageous to detect errors early. Several methods have been proposed to detect erroneous reasoning quickly based on the features of the forward pass of the language model that performs reasoning. In this work, we study whether the directed Forman curvature of that model's attention graph, a local quantity computed at an edge from the attention weights around it, carries information about a step's correctness. To do so, we evaluate four per-step verifiers on ProcessBench with and without the curvature appended to their input. Appending curvature values improves the overall mean performance of all four verifiers. ReProbe, the verifier that takes every token of a step as input, shows the largest improvement. Adding the curvature increases the time of the language model's forward pass by 18% on average.