Mateusz Bagiński comments on Attribution-based parameter decomposition

[Mateusz Bagiński]

Then we train to match the original model’s output by minimising an MSE loss $L_{\text{minimality}}=\text{MSE}\left(f\right(x,{\theta }^{\ast }),f(x,\kappa \left(x\right)\left)\right)$

I think you wanted

$\text{MSE}\left(f\right(x|{\theta }^{\ast }),f(x|\kappa \left(x\right)\left)\right)$