Path-integral graph convolutions
Borrowing from physics to aggregate over molecular graphs
Most graph neural networks aggregate over a node’s immediate neighbours. A path-integral convolutional kernel instead sums over every path between two atoms, damping each one by its length — an idea lifted from physics.
I implemented it for the molhiv dataset on the Open Graph Benchmark, a drug-discovery task where the relationship between distant atoms genuinely matters. The implementation is deliberately lightweight: it trains on CPU, and moves to a GPU without changes.
Every path between two atoms contributes, weighted down by its length.