interpretation of regularization

Blue arrows indicate node feature vectors hv of the latent space, and the orange area/point indicate possible range of graph feature vector hG obtained by applying READOUT to hv. We elaborate our motivation behind orthogonal regularization (15) proposed in Section 4.2.3. The biggest motivation behind orthognoal regularization lies in understanding (8) and (12) that the node features H becomes full rank matrix with good condition number. Figure 5 visually demonstrates the geometric effect of attention-based READOUT and orthogonal regularization with two example node features h1 and h2. Only one graph feature vector hG is possible from the combination of two node features with conventional READOUT, while vectors within the range of the orange rhombus can represent the whole graph feature with attention-based READOUT. With orthogonal regularization, area of the range that the graph feature vector hG can represent become even larger, with lower possibility of null subspace within H. Accordingly, the subspace that H can span can be rich enough.