Scalable Linearized Laplace Approximation via Surrogate Neural Kernel

• URL: http://arxiv.org/abs/2601.21835v2
• Date: Tue, 03 Feb 2026 11:19:39 GMT
• Title: Scalable Linearized Laplace Approximation via Surrogate Neural Kernel
• Authors: Luis A. Ortega, Simón Rodríguez-Santana, Daniel Hernández-Lobato,
• Abstract summary: We introduce a scalable method to approximate the kernel of the Linearized Laplace Approximation (LLA)<n>We use a surrogate deep neural network (DNN) that learns a compact feature representation whose inner product replicates the Neural Tangent Kernel (NTK)
• Score: 11.227924985781423
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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