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arXiv · 2601.21835

Scalable Linearized Laplace Approximation via Surrogate Neural Kernel

Luis A. Ortega·Simón Rodríguez-Santana·Daniel Hernández-Lobato
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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.

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Luis A. Ortega, Simón Rodríguez-Santana, Daniel Hernández-Lobato. 2026-01-29. Scalable Linearized Laplace Approximation via Surrogate Neural Kernel. https://arxiv.org/abs/2601.21835

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