# Aligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifold

arXiv: https://arxiv.org/abs/2601.22806 · HTML: https://mlsanity.com/paper/2601.22806/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [PTE: Predictive Text Embedding through Large-scale Heterogeneous Text Networks](https://mlsanity.com/paper/1508.00200/) (2015)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [Metrics for Probabilistic Geometries](https://mlsanity.com/paper/1411.7432/) (2014)
- [Learning Manifold Dimensions with Conditional Variational Autoencoders](https://mlsanity.com/paper/2302.11756/) (2023)
- [Keep It Simple: Graph Autoencoders Without Graph Convolutional Networks](https://mlsanity.com/paper/1910.00942/) (2019)
- [Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders](https://mlsanity.com/paper/1911.08147/) (2019)
- [Relation Learning on Social Networks with Multi-Modal Graph Edge Variational Autoencoders](https://mlsanity.com/paper/1911.05465/) (2019)
- [Random Geometric Graph: Some recent developments and perspectives](https://mlsanity.com/paper/2203.15351/) (2022)
- [Identifying Metric Structures of Deep Latent Variable Models](https://mlsanity.com/paper/2502.13757/) (2025)
- [Generating social networks with static and dynamic utility-maximization approaches](https://mlsanity.com/paper/2411.16464/) (2024)

## Abstract (arXiv)

The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This forces a destructive alignment that erodes information about the graph's underlying generative process. To recover this lost signal, we introduce a custom variational autoencoder that separates manifold learning from structural alignment. By quantifying the metric distortion needed to map the attribute manifold onto the graph's Heat Kernel, we transform geometric conflict into an interpretable structural descriptor. Experiments show our method uncovers connectivity patterns and anomalies undetectable by conventional approaches, proving both their theoretical inadequacy and practical limitations.