# Approximate Probabilistic Inference via Word-Level Counting

arXiv: https://arxiv.org/abs/1511.07663 · HTML: https://mlsanity.com/paper/1511.07663/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2015.

## Built on by (most cited first, 5 of 5)

- [Rounding Meets Approximate Model Counting](https://mlsanity.com/paper/2305.09247/) (2023)
- [On the Hardness of Approximating Distributions with Tractable Probabilistic Models](https://mlsanity.com/paper/2506.01281/) (2025)
- [Systematic Parameter Decision in Approximate Model Counting](https://mlsanity.com/paper/2504.05874/) (2025)
- [Approximate SMT Counting Beyond Discrete Domains](https://mlsanity.com/paper/2507.18612/) (2025)
- [CSB: A Counting and Sampling tool for Bit-vectors](https://mlsanity.com/paper/2607.04142/) (2026)

## Abstract (arXiv)

Hashing-based model counting has emerged as a promising approach for large-scale probabilistic inference on graphical models. A key component of these techniques is the use of xor-based 2-universal hash functions that operate over Boolean domains. Many counting problems arising in probabilistic inference are, however, naturally encoded over finite discrete domains. Techniques based on bit-level (or Boolean) hash functions require these problems to be propositionalized, making it impossible to leverage the remarkable progress made in SMT (Satisfiability Modulo Theory) solvers that can reason directly over words (or bit-vectors). In this work, we present the first approximate model counter that uses word-level hashing functions, and can directly leverage the power of sophisticated SMT solvers. Empirical evaluation over an extensive suite of benchmarks demonstrates the promise of the approach.