dgl.svd_pe¶
-
dgl.
svd_pe
(g, k, padding=False, random_flip=True)[source]¶ SVD-based Positional Encoding, as introduced in Global Self-Attention as a Replacement for Graph Convolution
This function computes the largest \(k\) singular values and corresponding left and right singular vectors to form positional encodings.
- Parameters
g (DGLGraph) – A DGLGraph to be encoded, which must be a homogeneous one.
k (int) – Number of largest singular values and corresponding singular vectors used for positional encoding.
padding (bool, optional) – If False, raise an error when \(k > N\), where \(N\) is the number of nodes in
g
. If True, add zero paddings in the end of encoding vectors when \(k > N\). Default : False.random_flip (bool, optional) – If True, randomly flip the signs of encoding vectors. Proposed to be activated during training for better generalization. Default : True.
- Returns
Return SVD-based positional encodings of shape \((N, 2k)\).
- Return type
Tensor
Example
>>> import dgl
>>> g = dgl.graph(([0,1,2,3,4,2,3,1,4,0], [2,3,1,4,0,0,1,2,3,4])) >>> dgl.svd_pe(g, k=2, padding=False, random_flip=True) tensor([[-6.3246e-01, -1.1373e-07, -6.3246e-01, 0.0000e+00], [-6.3246e-01, 7.6512e-01, -6.3246e-01, -7.6512e-01], [ 6.3246e-01, 4.7287e-01, 6.3246e-01, -4.7287e-01], [-6.3246e-01, -7.6512e-01, -6.3246e-01, 7.6512e-01], [ 6.3246e-01, -4.7287e-01, 6.3246e-01, 4.7287e-01]])