# LF-PPL: A Low-Level First Order Probabilistic Programming Language for Non-Differentiable Models

arXiv: https://arxiv.org/abs/1903.02482 · HTML: https://mlsanity.com/paper/1903.02482/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Designing Perceptual Puzzles by Differentiating Probabilistic Programs](https://mlsanity.com/paper/2204.12301/) (2022)
- [Nonparametric Hamiltonian Monte Carlo](https://mlsanity.com/paper/2106.10238/) (2021)
- [Guaranteed Bounds for Posterior Inference in Universal Probabilistic Programming](https://mlsanity.com/paper/2204.02948/) (2022)

## Abstract (arXiv)

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.