Approximate Bayesian Inference via Bitstring Representations

TL;DR

This paper introduces a scalable method for approximate Bayesian inference using bitstring representations, enabling probabilistic modeling in quantized parameter spaces with efficient and interpretable results.

Contribution

It presents a novel approach to perform Bayesian inference in discrete, quantized spaces using probabilistic circuits, advancing scalable and interpretable machine learning.

Findings

Efficient inference in quantized neural networks demonstrated.

Probabilistic circuits enable tractable learning in discrete spaces.

Method maintains accuracy while improving scalability.

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.