Detail the steps involved in implementing a graph attention network (GAT) from scratch.

Example Answer

I would first fix the edge direction convention and include self-loops if the architecture requires them. For each head, I linearly transform node features, compute a learned score for each permitted recipient-neighbor pair, apply LeakyReLU, and normalize with a softmax over that recipient's neighborhood only. Then I take the attention-weighted sum of neighbor features.

Intermediate heads are usually concatenated; a final layer can average them. I would train the projection and attention parameters with the task loss, and handle dropout and train/evaluation modes explicitly. Attention changes the weights of existing permitted messages; it does not automatically discover new graph edges or provide a faithful explanation.

Before training, I would check a tiny graph: each neighborhood's weights sum to one, non-neighbors contribute nothing, and changing node ordering leaves the appropriately reordered outputs unchanged. A dense all-pairs implementation is useful for a toy check but scales poorly; production message passing should process the actual edges.

Worked Example

One scalar head with fixed toy parameters, showing the forward aggregation only:

import math
h = [1.0, 2.0, 3.0]  # already projected features
neighbors = [[0, 1], [0, 1, 2], [1, 2]]  # includes self
out = []
for i, js in enumerate(neighbors):
    scores = [max(h[i] + h[j], 0.2 * (h[i] + h[j])) for j in js]
    weights = [math.exp(s - max(scores)) for s in scores]
    out.append(sum(w * h[j] for w, j in zip(weights, js)) / sum(weights))
print([round(v, 3) for v in out])  # [1.731, 2.575, 2.731]

Original GAT