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title: Geometric Deep Learning
tags: [object]

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# Geometric Deep Learning 

## Papers 

- [Geometric Deep Learning](https://arxiv.org/pdf/2104.13478.pdf) - Bible Book 
    - [website](https://geometricdeeplearning.com/) 
    - [lecture recordings](https://geometricdeeplearning.com/lectures/) 
- [Thesis- E(2) - Equivariant Steerable CNNs](https://gabri95.github.io/Thesis/thesis.pdf)


## Resources for group theory 
- [Visual Group Theory Lecture](http://www.math.clemson.edu/~macaule/classes/m19_math4120/) 
- [Visual tools](https://nathancarter.github.io/group-explorer/GroupExplorer.html) 
- [Introduction to Group Theory with problem and solutions](https://mathdoctorbob.org/UReddit.html) 
## People 
- [Taco Cohen](https://tacocohen.wordpress.com/) 
    - papers in medical images 
        - [Rotation Equivariant CNNs for Digital Pathology](https://arxiv.org/pdf/1806.03962.pdf) 
        - [Pulmonary Nodule Detection in CT Scans with Equivariant CNNs](https://marysia.nl/assets/MIA.pdf) 
        - [3D G-CNNs for Pulmonary Nodule Detection](https://arxiv.org/pdf/1804.04656.pdf)

- [Max Welling](https://staff.fnwi.uva.nl/m.welling/) 
    - Geometric deep learning 
    - Application in biology, chemistry, physics, medical fields. 


### talk 
Geometry is the study of invariants or symmetries, the properties that remain unchanged under some class of transformations (group). 

![](https://i.imgur.com/gg6m7YK.png)

This can be helpful in providing a constructive procedure to build neural network architectures in a principled way. 




## Lecture 5 Graphs and Sets I 

### permutation invariant and equivariant over set 
invariant: $f(\textbf{PX})=f(\textbf{X})$
$f(\textbf{X})=\phi(\oplus_{i\in V}\psi(\textbf{x}_i))$
$\oplus$ might be sum, max, average operators. 
Equivariant: $\textbf{F}(\textbf{PX})=\textbf{P}\textbf{F}(\textbf{X})$, $\textbf{F}$ takes a matrix as input and output an matrix. 

### permutation invariant and equivariant over graph 
invariant: $f(\textbf{PX}, \textbf{PAP}^T)=f(\textbf{X})$
Equivariant: $\textbf{F}(\textbf{PX}, \textbf{PAP}^T)=\textbf{P}\textbf{F}(\textbf{X, A})$, $\textbf{F}$ takes a matrix as input and output an matrix.  

Prove: 
$convolutional\subseteq attentional\subseteq message$-$passing$. 

### Transformers are GNN 
- fully connected graph GAT  
- Why are transformers sequence based? Because the positional embeddings are injected into features, i.e., the sin and cos tell you what position this node in the sequence. 
- If we drop those positional embeddings, you will have the same fully connected GAT. 












