Adrian Robert Minut, Nico Daheim, Marco Miani, Mohammad Emtiyaz Khan, Wu Lin, Thomas Möllenhoff
原文摘要
Structured weight-uncertainty can improve many aspects of deep learning, but it remains costly to estimate and difficult to implement. Here, we show that these issues can be addressed by adapting the SOAP optimizer. Our key idea is to run IVON, an existing diagonal-covariance variational method, in the eigenspace of SOAP's preconditioner and then use the preconditioner to transform the diagonal estimate into a non-diagonal covariance. The resulting method has costs similar to those of SOAP and requires no drastic changes to training pipelines. We call the posteriors obtained in this way SOAP-Bubbles and our new optimizer Eigenspace-VON (EVON). We show that, for logistic regression, EVON can match the full Gaussian covariance and that, for language model pretraining, it yields significantly better results than existing diagonal-covariance methods. Our work makes it easier to estimate more expressive posterior distributions for deep learning at scale.
A primary limitation of modern deep learning is the miscalibration of model confidence; traditional architectures fundamentally lack a mechanism to quantify their own uncertainty. Larger models and larger datasets mitigate this issue, but they do not resolve the underlying structural deficiency. Bayesian methods offer a principled uncertainty-aware learning framework through stochastic parameters. Yet, despite the established benefits, the inherent computational overhead often compromises either scalability or quality. This trade-off currently prevents the widespread adoption of Bayesian methods. This Thesis bridges the gap between high-quality and low-complexity by introducing a novel distribution on parameter space: a degenerate Gaussian whose covariance is a projection matrix aligned with the null space of the Fisher information matrix. We demonstrate the scalability of this Bayesian posterior through two numerically efficient algorithms: one for posterior sampling and another for the direct computation of predictive confidence. Empirically, we show State-Of-The-Art confidence calibration and out-of-distribution detection for large models. We provide theoretical grounding for this approach. We study the degeneracies inherent in Amari's information geometry and highlight its most relevant component: the split of parameter's perturbations into two orthogonal subspaces. From this perspective, our posterior naturally emerges as the simplest choice that captures this split, assigning unitary variance to one subspace and zero variance to the other. Moreover, through the tools of differential geometry, we utilize this split to identify and rectify a critical misalignment issue of the non-linearized Laplace Approximation. Finally, with a focus on PAC-Bayes generalization bounds, we pave the way for a deeper understanding of the learning capabilities of overparametrized models.