Calibrating your confidence requires thinking of all the ways you could be wrong

Marco Miani

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…