# Scalable Linearized Laplace Approximation via Surrogate Neural Kernel

arXiv: https://arxiv.org/abs/2601.21835 · HTML: https://mlsanity.com/paper/2601.21835/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 7 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 5 of 5)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [Accelerated Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2210.12642/) (2022)
- [Variational Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2302.12565/) (2023)
- [Fixed-Mean Gaussian Processes for Post-hoc Bayesian Deep Learning](https://mlsanity.com/paper/2412.04177/) (2024)

## Built on by (most cited first, 2 of 2)

- [VOLTA: The Surprising Ineffectiveness of Auxiliary Losses for Calibrated Deep Learning](https://mlsanity.com/paper/2604.08639/) (2026)
- [Contrastive Linearized Laplace: Loss Geometry, Valid Repairs, and Reliable Cores](https://mlsanity.com/paper/2610.14875/) (2026)

## Abstract (arXiv)

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.