torch_geometric.nn.norm.PairNorm

class PairNorm(scale: float = 1.0, scale_individually: bool = False, eps: float = 1e-05)

Bases: Module

Applies pair normalization over node features as described in the “PairNorm: Tackling Oversmoothing in GNNs” paper.

\[ \begin{align}\begin{aligned}\begin{split}\mathbf{x}_i^c &= \mathbf{x}_i - \frac{1}{n} \sum_{i=1}^n \mathbf{x}_i \\\end{split}\\\mathbf{x}_i^{\prime} &= s \cdot \frac{\mathbf{x}_i^c}{\sqrt{\frac{1}{n} \sum_{i=1}^n {\| \mathbf{x}_i^c \|}^2_2}}\end{aligned}\end{align} \]

Parameters:

• scale (float, optional) – Scaling factor \(s\) of normalization. (default, 1.)

• scale_individually (bool, optional) – If set to True, will compute the scaling step as \(\mathbf{x}^{\prime}_i = s \cdot \frac{\mathbf{x}_i^c}{{\| \mathbf{x}_i^c \|}_2}\). (default: False)

• eps (float, optional) – A value added to the denominator for numerical stability. (default: 1e-5)

forward(x: Tensor, batch: Optional[Tensor] = None, batch_size: Optional[int] = None) → Tensor

Forward pass.

Parameters:

• x (torch.Tensor) – The source tensor.

• batch (torch.Tensor, optional) – The batch vector \(\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N\), which assigns each element to a specific example. (default: None)

• batch_size (int, optional) – The number of examples \(B\). Automatically calculated if not given. (default: None)