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DeepProbLog: Neural Probabilistic Logic Programming

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

 Institutions

🎓KU LeuvenLeuven · Belgium20 works · 5,325 citations🎓Ghent UniversityGhent · Belgium14 works · 2,565 citations🎓Cardiff UniversityCardiff · United Kingdom8 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. DOI 10.48550/arxiv.1805.10872 · arXiv 1805.10872

@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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