Weighted Edge Message Passing

[MarcosZ]

I've read a couple of questions about attempting to leverage weights in edges, but through the current model I'm using I'm unsure how to do so.

$μ_v^{(t+1)} ←relu(θ_1 x +θ_2 \sum_{u \in N(v)} μ_u^{(t)} +θ_3 \sum_{u \in N(v)} relu(θ_4 w(v,u))$

The above equation is what I'm attempting to replicate and I believe that the standard MessagePassing layer has what I need with regards to the first two pieces of the equation. I'm using a GeneralConv layer to accomplish this with 4 hops of message passing.

What I'm trying to accomplish is adding the last portion which takes into consideration the edge weights, but have been unsuccessful so far.

What I've tried:

• editing the MessagePassing layer to add another aggregation step of edge weights
• looking into other layers to see if any could help (ECCConv) being the closest.

For context, I've been using the GeneralGNN model and it has worked well on low complexity. However, I think it's not as successful anymore as I increase the graph sizes because it doesn't consider edge weight difference.

Any ideas on how I could go about incorporating edge weight into the GeneralGNN model?

[MarcosZ]

I seem to have gotten edge weights to be incorporated through redefining MessagePassing and GeneralConv to generate another message specifically for edge weights. However, I'm not sure if this is the best way. Still looking for ideas.

[MarcosZ]

The solution here seems to be to add edge weights as an edge attribute and generate another message in a custom MessagePassing layer. It will look like this in your propagate() function, where e is an array the same dimensions as x, your node attributes, but has your edge weights per neighbor.

# Edge Message
msg_kwargs = self.get_kwargs(x, a, e, self.msg_signature, kwargs)
message_e = self.message(e, **msg_kwargs)

# Aggregate
agg_kwargs = self.get_kwargs(x, a, e, self.agg_signature, kwargs)
weights = self.aggregate(message_e, **agg_kwargs)

# Update
upd_kwargs = self.get_kwargs(x, a, e, self.upd_signature, kwargs)
output = self.update(embeddings, **upd_kwargs)

I then return both the embedding aggregation and the edge weight aggregation from propagate().