HouseGNN Mitigates Oversmoothing in Deep Graph Neural Networks

Deep Graph Neural Networks (GNNs) often suffer from "oversmoothing," a phenomenon where node representations become increasingly similar and lose distinct information as the network depth increases. This occurs because the normalized graph propagation operator repeatedly applies directly to hidden representations, leading to a collapse into a low-information subspace. To combat this, researchers propose the Householder Graph Neural Network (HouseGNN). Unlike standard GCNs that directly update hidden states, HouseGNN uses aggregated neighborhood messages solely to estimate a reflection direction. Node embeddings are then updated via a Householder reflector, followed by GroupSort, creating a piecewise orthogonal layer. This design ensures that every internal layer preserves the node-wise Euclidean norm, preventing the progressive collapse of information. The Householder reflector is also scale and sign-invariant in the message, and while pairwise distances can change, the overall mechanism effectively mitigates oversmoothing, allowing for deeper and more expressive GNN architectures.