Relational Deep Learning

Relational Tables to Graphs¶

Given the tables:

• Users

  user_id
  U1
  U2

• Products

  product_id
  P1
  P2

• Sales

  sale_id	user_id	product_id	price
  S1	U1	P1	20
  S2	U1	P2	80
  S3	U2	P1	15

1. Construct the relational entity graph. What are the nodes and edges?

2. What node types and edge types exist?

3. Where does the price live in the graph representation?

Graph Generation¶

Graph Generative Models¶

Assume that we are given a set of graphs $\{x_i\}$ sampled from $p_{\text{data}}(x)$ (which is unknown to us) and we want to generate more graphs similar to what we have.

1. What do we learn from the data in this case?

2. What is the objective that we maximize/minimize?

3. After training, how do we generate a new graph from the model?

4. In our case each $x$ is a graph. What extra difficulty appears when $x$ is a graph rather than a fixed-size vector? Name one issue.

Geometric Deep Learning¶

We want to predict a chemical property of a molecule (e.g., solubility in water). We have a set of molecules represented with graphs. For each molecule, we also know the coordinates of the atoms in that molecule.

We train a GNN on these graphs and obtain good predictive performance.

Given that, answer the following:

1. What happens if we rotate every molecule in the test set by 90°?

   (a) Does the true solubility of the molecules change?

   (b) Do the predictions of a regular GNN change? Why is this a problem?

2. Would augmenting the training set with randomly rotated molecules help? Why or why not?

3. How do geometric GNNs solve this issue?