# Geometric Deep Learning: a Temperature Based Analysis of Graph Neural Networks

arXiv: https://arxiv.org/abs/2309.00699 · HTML: https://mlsanity.com/paper/2309.00699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks](https://mlsanity.com/paper/1710.11029/) (2017)
- [Superpixel Image Classification with Graph Attention Networks](https://mlsanity.com/paper/2002.05544/) (2020)
- [MoNet: Moments Embedding Network](https://mlsanity.com/paper/1802.07303/) (2018)
- [A geometric interpretation of stochastic gradient descent using diffusion metrics](https://mlsanity.com/paper/1910.12194/) (2019)

## Abstract (arXiv)

We examine a Geometric Deep Learning model as a thermodynamic system treating the weights as non-quantum and non-relativistic particles. We employ the notion of temperature previously defined in [7] and study it in the various layers for GCN and GAT models. Potential future applications of our findings are discussed.