spd_learn.functional.spd_rebiasing#

spd_learn.functional.spd_rebiasing(X: Tensor, bias_sqrt: Tensor) → Tensor[source]#

Apply learnable rebiasing to centered SPD matrices.

Applies a congruence transformation to rebias centered SPD matrices:

\[\hat{X}_i = B^{1/2} X_i B^{1/2}\]

This corresponds to parallel transport from the identity to the bias matrix \(B\) under the affine-invariant Riemannian metric.

Parameters:

X (torch.Tensor) – Batch of centered SPD matrices with shape (…, n, n).
bias_sqrt (torch.Tensor) – Square root of the bias SPD matrix with shape (…, n, n).

Returns:

Rebiased SPD matrices with shape (…, n, n).

Return type:

torch.Tensor