# Geometric deep learning: going beyond Euclidean data

arXiv: https://arxiv.org/abs/1611.08097 · HTML: https://mlsanity.com/paper/1611.08097/

## Key facts

- Cited by 1,048 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2016.

## Built on by (most cited first, 30 of 1048)

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- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
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- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)
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- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
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## Abstract (arXiv)

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.