Adapting the Linearised Laplace Model Evidence for Modern Deep Learning
This work addresses a specific issue in Bayesian deep learning for researchers, offering incremental improvements to enhance the reliability of model selection and uncertainty estimation.
The paper tackled the poor interaction between the linearised Laplace method for model uncertainty and modern deep learning tools like stochastic approximation and normalization layers, providing theoretical and empirical recommendations to adapt the method, validated across various architectures including MLPs, CNNs, residual networks, autoencoders, and transformers.
The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.