Semantically-Regularized Logic Graph Embeddings

In this work, we aim to utilize prior knowledge encoded as logical rules to improve the performance of deep models. We propose a logic graph embedding network that projects d-DNNF formulae (and assignments) onto a manifold via an augmented Graph Convolutional Network (GCN). To generate semantically-faithful embeddings, we propose techniques to recognize node heterogeneity, and semantic regularization that incorporate structural constraints into the embedding. Experiments show that our approach improves the performance of models trained to perform model-checking and visual relation prediction.

[1]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[2]  Richard Evans,et al.  Can Neural Networks Understand Logical Entailment? , 2018, ICLR.

[3]  Adnan Darwiche,et al.  New Advances in Compiling CNF into Decomposable Negation Normal Form , 2004, ECAI.

[4]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[5]  Kai-Uwe Kühnberger,et al.  Neural-Symbolic Learning and Reasoning: A Survey and Interpretation , 2017, Neuro-Symbolic Artificial Intelligence.

[6]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[7]  Eric P. Xing,et al.  Harnessing Deep Neural Networks with Logic Rules , 2016, ACL.

[8]  Artur S. d'Avila Garcez,et al.  Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge , 2016, NeSy@HLAI.

[9]  Demis Hassabis,et al.  Mastering the game of Go without human knowledge , 2017, Nature.

[10]  Joao Marques-Silva,et al.  PySAT: A Python Toolkit for Prototyping with SAT Oracles , 2018, SAT.

[11]  Pierre Vandergheynst,et al.  Wavelets on Graphs via Spectral Graph Theory , 2009, ArXiv.

[12]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[13]  Stefano Ermon,et al.  Label-Free Supervision of Neural Networks with Physics and Domain Knowledge , 2016, AAAI.

[14]  Alexander M. Rush,et al.  Character-Aware Neural Language Models , 2015, AAAI.

[15]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.

[16]  Guy Van den Broeck,et al.  A Semantic Loss Function for Deep Learning with Symbolic Knowledge , 2017, ICML.

[17]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[18]  Guy Van den Broeck,et al.  Learning Logistic Circuits , 2019, AAAI.

[19]  Bram van Ginneken,et al.  A survey on deep learning in medical image analysis , 2017, Medical Image Anal..

[20]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[21]  Yiannis Demiris,et al.  Learning assistance by demonstration , 2015, J. Hum. Robot Interact..

[22]  Phong Le,et al.  Compositional Distributional Semantics with Long Short Term Memory , 2015, *SEMEVAL.

[23]  Hongyu Guo,et al.  Long Short-Term Memory Over Recursive Structures , 2015, ICML.

[24]  Harold Soh,et al.  Hyperprior Induced Unsupervised Disentanglement of Latent Representations , 2018, AAAI.

[25]  G. S. Tseitin.  On the Complexity of Derivation in Propositional Calculus , 1983 .

[26]  Jeffrey Pennington,et al.  GloVe: Global Vectors for Word Representation , 2014, EMNLP.

[27]  Seinosuke Toda,et al.  PP is as Hard as the Polynomial-Time Hierarchy , 1991, SIAM J. Comput..

[28]  Michael S. Bernstein,et al.  Visual Relationship Detection with Language Priors , 2016, ECCV.

[29]  Artur S. d'Avila Garcez,et al.  Logic Tensor Networks for Semantic Image Interpretation , 2017, IJCAI.

[30]  Sameer Singh,et al.  Injecting Logical Background Knowledge into Embeddings for Relation Extraction , 2015, NAACL.

[31]  Pushmeet Kohli,et al.  Learning Continuous Semantic Representations of Symbolic Expressions , 2016, ICML.

[32]  Thomas Demeester,et al.  Lifted Rule Injection for Relation Embeddings , 2016, EMNLP.

[33]  Christopher D. Manning,et al.  Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks , 2015, ACL.