---
title: "DeepProbLog: Neural Probabilistic Logic Programming — Manhaeve 2018"
description: "Inference grounds the program, builds a propositional formula, compiles it into an SDD and evaluates it bottom-up. 33 references, cited by 55 papers here."
authors: ["Robin Manhaeve", "Sebastijan Dumančić", "Angelika Kimmig", "Thomas Demeester", "Luc De Raedt"]
year: 2018
venue: "arXiv:1805.10872"
source: "https://arxiv.org/abs/1805.10872"
doi: "10.48550/arxiv.1805.10872"
arxiv: "1805.10872"
licence: "arXiv non-exclusive distribution license"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/manhaeve-2018-deepproblog-neural-probabilistic-logic/"
---
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# DeepProbLog: Neural Probabilistic Logic Programming

**Authors:** Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig, [Thomas Demeester](https://md.research.elamur.ai/free/en/authors/thomas-demeester/) and Luc De Raedt · **Year:** 2018 · **Venue:** arXiv:1805.10872 · **Licence:** [arXiv non-exclusive distribution license](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1805.10872) · [PDF](https://arxiv.org/pdf/1805.10872) · [DOI 10.48550/arxiv.1805.10872](https://doi.org/10.48550/arxiv.1805.10872) · [arXiv 1805.10872](https://arxiv.org/abs/1805.10872) · [OpenAlex](https://openalex.org/W2804796373)

**Citations:** 111 citations (OpenAlex, 2026-10-14) · [55](https://md.research.elamur.ai/free/en/papers/manhaeve-2018-deepproblog-neural-probabilistic-logic/cited-by/) in our library, of the 140,884 papers whose bibliographies we read

## Summary
Linking low-level perception, which neural networks handle well, with high-level probabilistic and logical reasoning is a long-standing open problem in AI. Instead of embedding reasoning inside a neural architecture, the authors start from the probabilistic logic programming language ProbLog and add "neural predicates." These are annotated disjunctions whose probabilities come from a network's normalized (softmax) output, such as a classifier for MNIST digits.

ProbLog's semantics, inference pipeline and implementation all carry over unchanged. Inference grounds the program, builds a propositional formula, compiles it into an SDD and evaluates it bottom-up. The real contribution is training. The semiring-based aProbLog computes gradients of a loss defined on query outputs, and these gradients are back-propagated into the networks. This tunes logic parameters and network weights together, using only query-level supervision.

Experiments cover MNIST addition, program induction and a probabilistic Coin-Urn task. They show that encoding background knowledge as rules lets a digit classifier be learned as a latent component. That classifier can then be reused, for example on multi-digit sums, without extra training. The work matters as a general neuro-symbolic language with well-defined, Turing-equivalent semantics. The supplied text omits the detailed experimental numbers.

## Key points
- A neural annotated disjunction has the form `nn(m_q, t, u) :: q(t,u1); …; q(t,un)`. Here m_q is any network (CNN, RNN, etc.) whose softmax output supplies the probabilities.
- Inference reuses ProbLog's four steps: grounding, conversion to a propositional formula, compilation into a Sentential Decision Diagram (SDD), and bottom-up evaluation. Gradients come from the algebraic extension aProbLog.
- The implementation integrates ProbLog2 with PyTorch. It uses gradient accumulation rather than true mini-batching, and the code is published at bitbucket.org/problog/deepproblog.
- The tasks are labelled T1–T5 and include:
  - MNIST digit addition, trained only on pairwise sums;
  - program-induction tasks using hyper-parameters from Bošnjak et al. (2017);
  - a Coin-Urn task with RGB colours perturbed by Gaussian noise (σ = 0.03, in HSV space) and MNIST "coins" (even digits = heads, odd digits = tails).
- According to the authors, differentiable Forth was applied to only part of these tasks (T3–T5). The approach of Rocktäschel & Riedel (2017) would plausibly cover only T1 and T5.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [AI & machine learning](https://md.research.elamur.ai/free/en/shelves/ai/)

## Institutions

- [KU Leuven](https://md.research.elamur.ai/free/en/universities/ku-leuven/) — University, Leuven, Belgium · 20 works · 5,325 citations
- [Ghent University](https://md.research.elamur.ai/free/en/universities/ghent-university/) — University, Ghent, Belgium · 14 works · 2,565 citations
- [Cardiff University](https://md.research.elamur.ai/free/en/universities/cardiff-university/) — University, Cardiff, United Kingdom · 8 works · 2,004 citations

## Cite

Cite as: Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig, Thomas Demeester and Luc De Raedt. 2018. DeepProbLog: Neural Probabilistic Logic Programming. arXiv:1805.10872.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{manhaeve2018deepproblog,
  title = {{DeepProbLog: Neural Probabilistic Logic Programming}},
  author = {Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig, Thomas Demeester and Luc {De Raedt}},
  year = {2018},
  doi = {10.48550/arxiv.1805.10872},
  eprint = {1805.10872},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1805.10872}
}
```

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## References

33 references, 3 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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