# Curvature Regularization to Prevent Distortion in Graph Embedding

arXiv: https://arxiv.org/abs/2011.14211 · HTML: https://mlsanity.com/paper/2011.14211/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2020.

## Built on by (most cited first, 8 of 8)

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- [Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning](https://mlsanity.com/paper/2302.05717/) (2023)
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- [Fast Multi-grid Methods for Minimizing Curvature Energy](https://mlsanity.com/paper/2204.07921/) (2022)
- [Multi-Hyperbolic Space-based Heterogeneous Graph Attention Network](https://mlsanity.com/paper/2411.11283/) (2024)
- [Metapath-based Hyperbolic Contrastive Learning for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2506.16754/) (2025)
- [Hyperbolic Heterogeneous Graph Transformer](https://mlsanity.com/paper/2601.08251/) (2026)
- [Understanding and Improving Noisy Embedding Techniques in Instruction Finetuning](https://mlsanity.com/paper/2605.23171/) (2026)

## Abstract (arXiv)

Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this proximity-preserving strategy: Graph topology patterns, while preserved well into an embedding manifold by preserving proximity, may distort in the ambient embedding Euclidean space, and hence to detect them becomes difficult for machine learning models. To address the problem, we propose curvature regularization, to enforce flatness for embedding manifolds, thereby preventing the distortion. We present a novel angle-based sectional curvature, termed ABS curvature, and accordingly three kinds of curvature regularization to induce flat embedding manifolds during graph embedding. We integrate curvature regularization into five popular proximity-preserving embedding methods, and empirical results in two applications show significant improvements on a wide range of open graph datasets.