# Differential equation and probability inspired graph neural networks for latent variable learning

arXiv: https://arxiv.org/abs/2202.13800 · HTML: https://mlsanity.com/paper/2202.13800/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 71 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Attention-based Graph Neural Network for Semi-supervised Learning](https://mlsanity.com/paper/1803.03735/) (2018)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [Incorporating Transformer and LSTM to Kalman Filter with EM algorithm for state estimation](https://mlsanity.com/paper/2105.00250/) (2021)
- [Bidirectional LSTM-CRF Attention-based Model for Chinese Word Segmentation](https://mlsanity.com/paper/2105.09681/) (2021)

## Built on by (most cited first, 1 of 1)

- [Attention-based CNN-LSTM and XGBoost hybrid model for stock prediction](https://mlsanity.com/paper/2204.02623/) (2022)

## Abstract (arXiv)

Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from observation. Subspace learning maps high-dimensional features on low-dimensional subspace to capture efficient representation. Graphs are widely applied for modeling latent variable learning problems, and graph neural networks implement deep learning architectures on graphs. Inspired by probabilistic theory and differential equations, this paper conducts notes and proposals about graph neural networks to solve subspace learning problems by variational inference and differential equation.