Intentionality of non-analytical gradient implementations for the 2D Mip filter

Ascertain whether the gradient computation strategies used in the Taming-3DGS and StopThePop re-implementations for the opacity compensation factor of the 2D Mip filter in Mip-Splatting (i.e., \hat{o} = sqrt(|Σ_2D|/|\hat{Σ}_2D|) · o) intentionally deviate from the analytical derivative with respect to the 2D covariance Σ_2D.

Background

Mip-Splatting introduces a 2D Mip filter for anti-aliasing that applies an opacity compensation factor depending on the original and dilated 2D covariance matrices. The authors observe that derivatives of this compensation factor with respect to Σ_2D can be numerically unstable, potentially causing exploding gradients.

While investigating implementations, the authors note that the original Mip-Splatting code clips extreme values, and that some re-implementations compute gradients in a way that does not match the analytical derivative. The authors explicitly state it is unclear whether this deviation is intentional, and they suggest detaching the compensation factor from the gradient computation as a practical remedy.