Attention-Graph Curvature for the Verification of Mathematical Reasoning

Kanghyeon Kim; Johannes F. Lutzeyer; Yanzhu Guo

Home/Archive/arXiv

arXiv · 2610.16709

Attention-Graph Curvature for the Verification of Mathematical Reasoning

Kanghyeon Kim·Johannes F. Lutzeyer·Yanzhu Guo

View original source ↗Read source document ↗Export metadata ↓

Abstract

Language models have recently solved open Erdős 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.

Explore related subjects

cs.LG cs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Kanghyeon Kim, Johannes F. Lutzeyer, Yanzhu Guo. 2026-10-12. Attention-Graph Curvature for the Verification of Mathematical Reasoning. https://arxiv.org/abs/2610.16709

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generation of data on discontinuous manifolds via continuous stochastic non-invertible networks

The generation of discontinuous distributions is a difficult task for most known frameworks such as generative autoencoders and generative adversarial networks. Generative non-invertible models are unable to accurately generate such distributions, require long training and often are subject to mode collapse. Variational autoencoders (VAEs), which are based on the idea of keeping the latent space to be Gaussian for the sake of a simple sampling, allow an accurate reconstruction, while they experience significant limitations at generation task. In this work, instead of trying to keep the latent space to be Gaussian, we use a pre-trained contrastive encoder to obtain a clustered latent space. Then, for each cluster, representing a unimodal submanifold, we train a dedicated low complexity network to generate this submanifold from the Gaussian distribution. The proposed framework is based on the information-theoretic formulation of mutual information maximization between the input data and latent space representation. We derive a link between the cost functions and the information-theoretic formulation. We apply our approach to synthetic 2D distributions to demonstrate both reconstruction and generation of discontinuous distributions using continuous stochastic networks.

cs.LG↗

arXiv2026

Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series

We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides calibrated prediction intervals. Unlike the existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. When the raw forecast intervals are approximately calibrated, we prove that BCI is near optimal for its surrogate model predictive control problem. We find empirically that BCI avoids uninformative intervals with infinite lengths under our main experimental configuration and generates substantially shorter prediction intervals when the raw forecast intervals are poorly calibrated.

cs.LG↗

arXiv2026

GLL: A Differentiable Graph Learning Layer for Neural Networks

Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.

cs.LG↗