Filippo Bigi^1*, Sanggyu Chong^1*, Michele Ceriotti^1*, Federico Grasselli^1*

1 COSMO, Institut des Matériaux, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Vaud, Switzerland

* Corresponding authors emails: filippo.bigi@epfl.ch, sanggyu.chong@epfl.ch, michele.ceriotti@epfl.ch, fede.grasselli@gmail.com

DOI10.24435/materialscloud:5r-rf [version v1]

Publication date: Oct 17, 2024

How to cite this record

Filippo Bigi, Sanggyu Chong, Michele Ceriotti, Federico Grasselli, A prediction rigidity formalism for low-cost uncertainties in trained neural networks, Materials Cloud Archive 2024.166 (2024), https://doi.org/10.24435/materialscloud:5r-rf

Description

Quantifying the uncertainty of regression models is essential to ensure their reliability, particularly since their application often extends beyond their training domain. Based on the solution of a constrained optimization problem, this work proposes ‘prediction rigidities’ as a formalism to obtain uncertainties of arbitrary pre-trained regressors. A clear connection between the suggested framework and Bayesian inference is established, and a last-layer approximation is developed and rigorously justified to enable the application of the method to neural networks. This extension affords cheap uncertainties without any modification to the neural network itself or its training procedure. The effectiveness of this approach is shown for a wide range of regression tasks, ranging from simple toy models to applications in chemistry and meteorology. This record includes computational experiments supporting the MLST paper titled "A prediction rigidity formalism for low-cost uncertainties in trained neural networks".

Materials Cloud sections using this data

Files

File name	Size	Description
llpr.zip MD5md5:70c0fb1fb3bce6f9147a65890f27ec7f	499.0 MiB	The zip file contains (1) an implementation of the proposed method and (2) all experiments associated with the manuscript. The archive can be navigated thanks to the readme files in each subfolder.

License

Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Keywords

machine learning MARVEL/P2 uncertainty quantification neural networks Laplace approximation prediction rigidity confidence interval regressors neural tangent kernel