Towards Efficient Posterior Sampling in Deep Neural Networks via Symmetry Removal (Extended Abstract)

MCML Authors

Lisa Wimmer

→ Group Bernd Bischl
 Statistical Learning and Data Science

Bernd Bischl

Prof. Dr.

Director

Statistical Learning and Data Science

Stephan Günnemann

Prof. Dr.

Principal Investigator

Data Analytics & Machine Learning

David Rügamer

Prof. Dr.

Principal Investigator

Statistics, Data Science and Machine Learning

Abstract

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are considered prohibitively expensive for large modern architectures. Local methods, which have emerged as a popular alternative, focus on specific parameter regions that can be approximated by functions with tractable integrals. While these often yield satisfactory empirical results, they fail, by definition, to account for the multi-modality of the parameter posterior. In this work, we argue that the dilemma between exact-but-unaffordable and cheap-but-inexact approaches can be mitigated by exploiting symmetries in the posterior landscape. Such symmetries, induced by neuron interchangeability and certain activation functions, manifest in different parameter values leading to the same functional output value. We show theoretically that the posterior predictive density in Bayesian neural networks can be restricted to a symmetry-free parameter reference set. By further deriving an upper bound on the number of Monte Carlo chains required to capture the functional diversity, we propose a straightforward approach for feasible Bayesian inference. Our experiments suggest that efficient sampling is indeed possible, opening up a promising path to accurate uncertainty quantification in deep learning.

inproceedings

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IJCAI 2024

33rd International Joint Conference on Artificial Intelligence. Jeju, Korea, Aug 03-09, 2024.

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Authors

J. G. Wiese • L. Wimmer • T. Papamarkou • B. Bischl • S. Günnemann • D. Rügamer

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Links

DOI

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Research Areas

 A1 | Statistical Foundations & Explainability

 A3 | Computational Models