There's a strong connection between the GAP sigmas and ACE weights. In principle weights are the square root inverse of the sigmas, but I don't think it's quite as simple. One can dial the weights up for a very simple ACE model, but this will not lead to good training errors as the ACE model is too constrainted to fit the underlying data. Using ARD/BRR this would become apparent because the associated noise term would be large. I think it'd be nice to propagate the noise term through the weights matrix and display the "optimised sigmas" after an ACE fit. GAP users should relate to this quite well I think.
There's a strong connection between the GAP sigmas and ACE weights. In principle weights are the square root inverse of the sigmas, but I don't think it's quite as simple. One can dial the weights up for a very simple ACE model, but this will not lead to good training errors as the ACE model is too constrainted to fit the underlying data. Using ARD/BRR this would become apparent because the associated noise term would be large. I think it'd be nice to propagate the noise term through the weights matrix and display the "optimised sigmas" after an ACE fit. GAP users should relate to this quite well I think.