Exercises and Assignments

Pen and Paper: Convolve by Hand, Then Run the WL Test

You work this in class, before any of it is named. Both halves are things you can only really believe once you have done them with a pencil.

• Convolution and the Weisfeiler-Lehman Test (handed out in class; the PDF is being rewritten): slide a 3\times3 kernel over a small image and read off what it detects; then run the WL test by hand on labelled graphs, on unlabelled ones, and finally on a pair it cannot tell apart — which is the exact ceiling on what any message-passing GNN can do. The last part maps each WL step onto the corresponding piece of a GCN layer.

Hands-on Notebook

The runnable work for this module is on the hands-on page: a hand-designed spectral filter on the karate club, then a GCN trained on eight labelled nodes. A separate practice notebook builds a GCN for node classification from a blank cell:

• exercise-m09-graph-neural-net.py, in notebooks/m09-graph-neural-nets/ — run it locally with marimo edit; PyTorch does not run in the browser.

Assignments

Neither graded assignment runs in this module. The Pair Notebook and the Group Mini-Project both cover Modules 2 through 6. The worksheet and the notebook above are practice, not submissions.