  Graph Neural Network (GNN) ushered in a new era of machine learning with
interconnected datasets. While traditional neural networks can only be trained
on independent samples, GNN allows for the inclusion of inter-sample
interactions in the training process. This gain, however, incurs additional
memory cost, rendering most GNNs unscalable for real-world applications
involving vast and complicated networks with tens of millions of nodes (e.g.,
social circles, web graphs, and brain graphs). This means that storing the
graph in the main memory can be difficult, let alone training the GNN model
with significantly less GPU memory. While much of the recent literature has
focused on either mini-batching GNN methods or quantization, graph reduction
methods remain largely scarce. Furthermore, present graph reduction approaches
have several drawbacks. First, most graph reduction focuses only on the
inference stage (e.g., condensation and distillation) and requires full graph
GNN training, which does not reduce training memory footprint. Second, many
methods focus solely on the graph's structural aspect, ignoring the initial
population feature-label distribution, resulting in a skewed post-reduction
label distribution. Here, we propose a Feature-Label COnstrained graph Net
collapse, FALCON, to address these limitations. Our three core contributions
lie in (i) designing FALCON, a topology-aware graph reduction technique that
preserves feature-label distribution; (ii) implementation of FALCON with other
memory reduction methods (i.e., mini-batched GNN and quantization) for further
memory reduction; (iii) extensive benchmarking and ablation studies against
SOTA methods to evaluate FALCON memory reduction. Our extensive results show
that FALCON can significantly collapse various public datasets while achieving
equal prediction quality across GNN models. Code:
https://github.com/basiralab/FALCON
