Scalable Linearized Laplace Approximation via Surrogate Neural Kernel

We introduce a scalable method to approximate the kernel of the Linearized Laplace Approximation (LLA). For this, we use a surrogate deep neural network (DNN) that learns a compact feature representation whose inner product replicates the Neural Tangent Kernel (NTK). This avoids the need to compute large Jacobians. Training relies solely on efficient Jacobian-vector products, allowing to compute predictive uncertainty on large-scale pre-trained DNNs. Experimental results show similar or improved uncertainty estimation and calibration compared to existing LLA approximations. Notwithstanding, biasing the learned kernel significantly enhances out-of-distribution detection. This remarks the benefits of the proposed method for finding better kernels than the NTK in the context of LLA to compute prediction uncertainty given a pre-trained DNN.

Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learning

Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original network by adding output confidence measures, such as error bars, without compromising its initial accuracy. In this context, we introduce a novel family of sparse variational Gaussian processes (GPs), where the posterior mean is fixed to any continuous function when using a universal kernel. Specifically, we fix the mean of this GP to the output of the pre-trained DNN, allowing our approach to effectively fit the GP's predictive variances to estimate the DNN prediction uncertainty. Our approach leverages variational inference (VI) for efficient stochastic optimization, with training costs that remain independent of the number of training points, scaling efficiently to large datasets such as ImageNet. The proposed method, called fixed mean GP (FMGP), is architecture-agnostic, relying solely on the pre-trained model's outputs to adjust the predictive variances. Experimental results demonstrate that FMGP improves both uncertainty estimation and computational efficiency when compared to state-of-the-art methods.