# Notes on: Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., & Dahl, G. E. (2017): Neural message passing for quantum chemistry

## Table of Contents

## Terminology

- density functional theory (DFT)
- quantum mechianical simulation method

## Message Passing Neural Networks (MPNNs)

- Operate on undirected graphs with node features and edge features
- Runs for time stemps
- Defined in terms of message functions and vertex update functions
hidden states at each node in the graph are updated base on messages according to

where in the sum, denotes the neighbors of

**Readout phase**computes a feature vector for the whole grap using some readout function according to**Learned:**message functions , vertex update functions , and readout functon are all learned differentiable functions

Could also learn *edge features* in the graph and updating them analogously to the update equations above.

### Other research framed in the form of MPNNs

#### Kipf & Welling (2016)

In this case we have:

Checkout the supplementary material (section 10.1.1) in gilmer17_neural_messag_passin_quant_chemis for a the specific deduction of why kipf16_semi_super_class_with_graph_convol_networ corresponds to a MPNN! It's great.

- [kipf16_semi_super_class_with_graph_convol_networ] Kipf & Welling, Semi-Supervised Classification With Graph Convolutional Networks,
*CoRR*, (2016). link. - [gilmer17_neural_messag_passin_quant_chemis] Gilmer, Schoenholz, Riley, Patrick, Vinyals & Dahl, Neural Message Passing for Quantum Chemistry,
*CoRR*, (2017). link.