DeepProbLog: Neural Probabilistic Logic Programming Robin Manhaeve, - - PowerPoint PPT Presentation

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DeepProbLog: Neural Probabilistic Logic Programming Robin Manhaeve, - - PowerPoint PPT Presentation

May 20, 2023 400 likes •556 views

DeepProbLog: Neural Probabilistic Logic Programming Robin Manhaeve, Sebastijan Dumani , Angelika Kimmig, Thomas Demeester*, Luc De Raedt* * Joint last authors Real-life problems involve two important aspects. Sub-symbolic perception

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Robin Manhaeve, Sebastijan Dumančić, Angelika Kimmig, Thomas Demeester*, Luc De Raedt*

DeepProbLog: Neural Probabilistic Logic Programming

* Joint last authors

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DTAI reserach group

Real-life problems involve two important aspects.

Geiger, Andreas, et al. "Vision meets robotics: The KITTI dataset." The International Journal of Robotics Research (2013)

Reasoning with knowledge under uncertainty Sub-symbolic perception

Stop in front of a red light Obey the speed limit Be in the correct lane …

Deep Learning Probabilistic logic program

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P( light = red) = 0.9 P( obj1 = car ) = 0.8 P( obj1 turn right) = 0.7

DeepProbLog

ProbLog

= ProbLog + neural predicate

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The neural predicate

0,25 0,5 0,75 1 1 2 3 4 5 6 7 8 9

Classifier with softmax

  • Classifier defines a probability distribution over its output
  • Uncertainty in the prediction
  • Neural predicate: output = probabilistic choices in program
  • No changes needed in the ProbLog inference or its semantics
  • ProbLog can natively calculate the gradient

Probability distribution

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Perception

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ProbLog

Perception

Stop in front of a red light Obey the speed limit Be in the correct lane P( light = red) = 0.9

Reasoning

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ProbLog

Perception

Stop in front of a red light Obey the speed limit Be in the correct lane P( light = red) = 0.9 P( obj1 = car ) = 0.8 P( obj1 turn right) = 0.7

Neural predicate

Reasoning

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  • Neural-symbolic integration (Garcez)
  • Logical constraints as a regularizer (Xu, Diligenti, …)
  • Differentiable logical framework (Rocktäschel and Riedel, Evans and Grefenstette)
  • Differentiable interpreters (Graves, Bosnjak)
  • …

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Related work

Related work DeepProbLog Logic is made less expressive Full expressivity is retained Logic is pushed into the neural part Clean separation Fuzzy logic Probabilistic logic Language semantics is unclear Clear semantics

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  • Only labeled sums, not single digits
  • Train using only neural networks? Not suited!
  • DeepProbLog can solve this:
  • Neural predicate
  • From pixels to distribution over digits
  • NN trained from scratch
  • Logic:
  • Combine predictions into larger numbers
  • Perform addition

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Example task: MNIST addition + = ?

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Combined reasoning

Unknown distribution

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Combined reasoning

0.7::Red 0.8::Blue 0.6::Heads

Unknown distribution Perception

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Combined reasoning

0.7::Red 0.8::Blue 0.6::Heads Rules 0.7 :: win

Unknown distribution Perception Logical inference

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Combined reasoning

0.7::Red 0.8::Blue 0.6::Heads Rules 0.7 :: win

Unknown distribution Perception Logical inference Loss

Backpropagation

Update parameters Train NN

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Conclusion

DeepProbLog: Neural Probabilistic Logic Programming

  • Integration of DL and PLP
  • Probabilistic
  • Clean semantics, clear separation
  • Retain power of both worlds
  • Power of ProbLog

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Poster #118

Code is available at: https://bitbucket.org/problog/deepproblog