Approximate Bayesian Inference via Bitstring Representations

Aleksanteri Sladek, Martin Trapp, Arno Solin

Keywords: Approximate inference, Quantization, Tractable models, Probabilistic circuits

TL;DR: We turn continuous parameters into discrete bitstrings for probabilistic inference

Abstract: The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex distributions and provides clear insights into model behavior. We validate our approach with various models, demonstrating inference efficiency without sacrificing accuracy. This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.

Code Link: www.github.com/AaltoML/bitvi

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission818/Authors, auai.org/UAI/2025/Conference/Submission818/Reproducibility_Reviewers

Submission Number: 818