Scalable Linearized Laplace Approximation via Surrogate Neural Kernel
Abstract
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.
Cite
@article{arxiv.2601.21835,
title = {Scalable Linearized Laplace Approximation via Surrogate Neural Kernel},
author = {Luis A. Ortega and Simón Rodríguez-Santana and Daniel Hernández-Lobato},
journal= {arXiv preprint arXiv:2601.21835},
year = {2026}
}
Comments
6 pages, 1 table. Accepted at European Symposium on Artificial Neural Networks (ESANN 2026) as oral presentation