  Gene regulatory relationships can be abstracted as a gene regulatory network
(GRN), which plays a key role in characterizing complex cellular processes and
pathways. Recently, graph neural networks (GNNs), as a class of deep learning
models, have emerged as a useful tool to infer gene regulatory relationships
from gene expression data. However, deep learning models have been found to be
vulnerable to noise, which greatly hinders the adoption of deep learning in
constructing GRNs, because high noise is often unavoidable in the process of
gene expression measurement. Can we preferably prototype a robust GNN for
constructing GRNs? In this paper, we give a positive answer by proposing a
Quadratic Graph Attention Network (Q-GAT) with a dual attention mechanism. We
study the changes in the predictive accuracy of Q-GAT and 9 state-of-the-art
baselines by introducing different levels of adversarial perturbations.
Experiments in the E. coli and S. cerevisiae datasets suggest that Q-GAT
outperforms the state-of-the-art models in robustness. Lastly, we dissect why
Q-GAT is robust through the signal-to-noise ratio (SNR) and interpretability
analyses. The former informs that nonlinear aggregation of quadratic neurons
can amplify useful signals and suppress unwanted noise, thereby facilitating
robustness, while the latter reveals that Q-GAT can leverage more features in
prediction thanks to the dual attention mechanism, which endows Q-GAT with the
ability to confront adversarial perturbation. We have shared our code in
https://github.com/Minorway/Q-GAT_for_Robust_Construction_of_GRN for readers'
evaluation.
