$\sigma$Transfer: Uncertainty Transfer from Small to Large Networks under $\mu\mathrm{P}$

תקציר מקורי באנגליתarXiv:2610.11668v1 Announce Type: cross Abstract: Reliable predictive uncertainty in Laplace approximations depends critically on the prior precision, yet selecting it requires a posterior sweep that is prohibitively expensive for neural networks with billions of parameters. Under the Maximal Update Parametrization ($\mu\mathrm{P}$), we derive a rescaling of the prior covariance that makes the selected precision stable as model width grows. This leads to $\sigma\mathrm{Transfer}$: we select the precision on a smaller model and zero-shot transfer it to the much larger model, i.e., without searching for the precision on the larger model at all. We show convergence of the prior kernel, posterior covariance, selected precision, and posterior-derived decisions under explicit conditions, and ver