var_mean

var_mean(x, rep_x)

Compute var() and mean() under symmetry constraints.

Parameters:

• x (Tensor) – (Tensor) samples with shape \((N,D_x)\) or \((N,D_x,T)\).

• rep_x (Representation) – (Representation) representation \(\rho_{\mathcal{X}}\).

Returns:

Tuple (var, mean) where mean is projected to \(\mathcal{X}^{\text{inv}}\) and variance satisfies irrep-wise isotropy in spectral basis.

Return type:

(Tensor, Tensor)

Shape:

• x: \((N,D_x)\) or \((N,D_x,T)\).

• Output: (var, mean) both with shape \((D_x,)\).

Note

This function reuses the same caches as mean() and var() when called repeatedly with the same representation object rep_x.