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Table B.2.

Summary of the GNN architecture for our fiducial five-feature model used in this work, with matrix dimensions for each layer.

Layer Type Input size Output size Description
Nodes × Features Nodes × Features
1 TransformerConv n × 5 n × 128 First GNN layer transforming input with n nodes of 5-dimensional features to 128-dimensional embedding for each node. n is between 7-48
2 BatchNorm1d n × 128 n × 128 Normalises the output of the first GNN layer.
3 ReLU n × 128 n × 128 Applies ReLU activation.
4 TransformerConv n × 128 n × 128 Second GNN layer refining 100-dimensional embeddings for each node.
5 BatchNorm1d n × 128 n × 128 Normalises the output of the second GNN layer.
6 ReLU n × 128 n × 128 Applies ReLU activation.
7 TransformerConv n × 128 n × 128 Third GNN layer refining 100-dimensional embeddings for each node.
8 BatchNorm1d n × 128 n × 128 Normalises the output of the second GNN layer.
9 ReLU n × 128 n × 128 Applies ReLU activation.
10 Global pooling n × 128 1 × 128 Aggregates node features into a single vector via global max pooling.
11 Concatenation (1 × 128)+(1 × 1) 1 × 129 Combines GAP output with an external feature (e.g. redshift).
12 Linear 1 × 129 1 × 60 Maps concatenated features to 60 dimensions.
13 BatchNorm1d 1 × 60 1 × 60 Normalises the output of the first linear layer.
14 ReLU 1 × 60 1 × 60 Applies ReLU activation.
15 Linear 1 × 60 1 × 30 Maps 60 features to 30 dimensions.
16 BatchNorm1d 1 × 30 1 × 30 Normalises the output of the second linear layer.
17 ReLU 1 × 30 1 × 30 Applies ReLU activation.
18 Linear 1 × 30 1 × 1 Final layer that outputs a single prediction value.

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