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  author    = {Jingyi Xu and
               Zilu Zhang and
               Tal Friedman and
               Yitao Liang and
               Guy Van den Broeck},
  title     = {A Semantic Loss Function for Deep Learning with Symbolic Knowledge},
  booktitle = {Proceedings of the 35th {ICML} 2018},
  year      = {2018},
}

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author = {Jones, D. S. (Douglas Samuel)},
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keywords = {Information theory},
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}

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}

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  year={2020}
}

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@inproceedings{shih2019smoothing,
  author    = {Andy Shih and
               Guy Van den Broeck and
               Paul Beame and
               Antoine Amarilli},
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  booktitle = {NeurIPS},
  year      = {2019}
}

@inproceedings{nishino2017,
	author = {Masaaki Nishino and Norihito Yasuda and Shin-ichi Minato and Masaaki Nagata},
	title = {Compiling Graph Substructures into Sentential Decision Diagrams},
	booktitle = {AAAI},
	year = {2017},
}

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  author={Diederik P. Kingma and Jimmy Ba},
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  year={2015},
  booktitle={ICLR}
}

@inproceedings{VergariNeurIPS21,
  author 	= {Vergari, Antonio and Choi, YooJung and Liu, Anji and Teso, Stefano and Van den Broeck, Guy},
  title     = {A Compositional Atlas of Tractable Circuit Operations for Probabilistic Inference},
  booktitle = {NeurIPS},
  year      = {2021},
}

@misc{dai2018tunneling,
      title={Tunneling Neural Perception and Logic Reasoning through Abductive Learning}, 
      author={Wang-Zhou Dai and Qiu-Ling Xu and Yang Yu and Zhi-Hua Zhou},
      year={2018},
      eprint={1802.01173},
      archivePrefix={arXiv},
      primaryClass={cs.AI}
}

@InProceedings{bosnjak2017programming,
  title = 	 {Programming with a Differentiable Forth Interpreter},
  author =       {Matko Bo{\v{s}}njak and Tim Rockt{\"a}schel and Jason Naradowsky and Sebastian Riedel},
  booktitle = 	 {Proceedings of the 34th ICML},
  year = 	 {2017},
}

@inproceedings{chang2007,
    title = "Guiding Semi-Supervision with Constraint-Driven Learning",
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      Roth, Dan",
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    year = "2007",
}

@inproceedings{rocktaschel2015,
    title = "Injecting Logical Background Knowledge into Embeddings for Relation Extraction",
    author = {Rockt{\"a}schel, Tim  and
      Singh, Sameer  and
      Riedel, Sebastian},
    booktitle = "Proceedings of the 2015 Conference of the NAACL",
    year = "2015",
}


@InProceedings{fischer19a,
  title = 	 {{DL}2: Training and Querying Neural Networks with Logic},
  author =       {Fischer, Marc and Balunovic, Mislav and Drachsler-Cohen, Dana and Gehr, Timon and Zhang, Ce and Vechev, Martin},
  booktitle = 	 {ICML},
  year = 	 {2019},
}

@inproceedings{grandvalet2005,
 author = {Grandvalet, Yves and Bengio, Yoshua},
 booktitle = {NeurIPS},
 title = {Semi-supervised Learning by Entropy Minimization},
 year = {2005}
}

@article{Valiant1979b,
title = {The complexity of computing the permanent},
journal = {Theoretical Computer Science},
year = {1979},
author = {L.G. Valiant},
}

@article{diligenti2017,
	author = {Diligenti, Michelangelo and Gori, Marco and Saccà, Claudio},
	journal = {Artificial Intelligence},
	title = {Semantic-based regularization for learning and inference},
	year = {2017},
}

@inproceedings{donadello2017,
  author    = {Ivan Donadello and Luciano Serafini and Artur d'Avila Garcez},
  title     = {Logic Tensor Networks for Semantic Image Interpretation},
  booktitle = {IJCAI},
  year      = {2017}
}

@inproceedings{manhaeve2018,
 author = {Manhaeve, Robin and Dumancic, Sebastijan and Kimmig, Angelika and Demeester, Thomas and De Raedt, Luc},
 booktitle = {NeurIPS},
 title = {DeepProbLog:  Neural Probabilistic Logic Programming},
 year = {2018}
}

@misc{dai2018,
      title={Tunneling Neural Perception and Logic Reasoning through Abductive Learning}, 
      author={Wang-Zhou Dai and Qiu-Ling Xu and Yang Yu and Zhi-Hua Zhou},
      year={2018},
      eprint={1802.01173},
      archivePrefix={arXiv},
      primaryClass={cs.AI}
}

@article{walker2006,
  title={ACE 2005 multilingual training corpus},
  author={Walker, Christopher and Strassel, Stephanie and Medero, Julie and Maeda, Kazuaki},
  journal={LDC},
  year={2006}
}

@inproceedings{luan2018,
    title = "Multi-Task Identification of Entities, Relations, and Coreference for Scientific Knowledge Graph Construction",
    author = "Luan, Yi  and
      He, Luheng  and
      Ostendorf, Mari  and
      Hajishirzi, Hannaneh",
    booktitle = "EMNLP",
    year = "2018",
}

@article{Zhong2020,
  author    = {Zexuan Zhong and
               Danqi Chen},
  title     = {A Frustratingly Easy Approach for Joint Entity and Relation Extraction},
  journal   = {CoRR},
  year      = {2020},
}

@inproceedings{
Pogancic2020,
title={Differentiation of Blackbox Combinatorial Solvers},
author={Marin Vlastelica Pogančić and Anselm Paulus and Vit Musil and Georg Martius and Michal Rolinek},
booktitle={ICLR},
year={2020},
}

@InProceedings{He2016,
author = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
title = {Deep Residual Learning for Image Recognition},
booktitle = {CVPR},
month = {June},
year = {2016}
}

@article{Valiant1979a,
author = {Valiant, Leslie G.},
title = {The Complexity of Enumeration and Reliability Problems},
journal = {SIAM Journal on Computing},
year = {1979},
}

@inproceedings{MaWa13a,
  author    = {Nicholas Mattei and Toby Walsh},
  title     = {PrefLib: A Library of Preference Data \textsc{http://preflib.org}},
  year      = {2013},
  booktitle = {ADT},
}

@inproceedings{Guo2020,
  title     = {Inference-Masked Loss for Deep Structured Output Learning},
  author    = {Guo, Quan and Rajaby Faghihi, Hossein and Zhang, Yue and Uszok, Andrzej and Kordjamshidi, Parisa},
  booktitle = {IJCAI},
  year      = {2020},
}
@article{Bach2017,
  author  = {Stephen H. Bach and Matthias Broecheler and Bert Huang and Lise Getoor},
  title   = {Hinge-Loss Markov Random Fields and Probabilistic Soft Logic},
  journal = {JMLR},
  year    = {2017},
}

@INPROCEEDINGS{Diligenti,
  author={Diligenti, Michelangelo and Roychowdhury, Soumali and Gori, Marco},
  booktitle={ICMLA}, 
  title={Integrating Prior Knowledge into Deep Learning}, 
  year={2017}
  }
  
 @inproceedings{Zhang2016,
    title = "Introducing {DRAIL} {--} a Step Towards Declarative Deep Relational Learning",
    author = "Zhang, Xiao  and
      Pacheco, Maria Leonor  and
      Li, Chang  and
      Goldwasser, Dan",
    booktitle = "Proceedings of the Workshop on Structured Prediction for {NLP}",
    year = "2016",
}

@inproceedings{hu2016,
    title = "Harnessing Deep Neural Networks with Logic Rules",
    author = "Hu, Zhiting  and
      Ma, Xuezhe  and
      Liu, Zhengzhong  and
      Hovy, Eduard  and
      Xing, Eric",
    booktitle = "ACL",
    year = "2016",
}

@inbook{Nandwani2019,
author = {Nandwani, Yatin and Pathak, Abhishek and Mausam and Singla, Parag},
title = {A Primal-Dual Formulation for Deep Learning with Constraints},
year = {2019},
booktitle = {NeurIPS},
}

@inproceedings{li2019,
    title = "Augmenting Neural Networks with First-order Logic",
    author = "Li, Tao  and
      Srikumar, Vivek",
    booktitle = "ACL",
    year = "2019"
}

@inproceedings{RaedtIJCAI2020,
  title     = {From Statistical Relational to Neuro-Symbolic Artificial Intelligence},
  author    = {De Raedt, Luc and Dumančić, Sebastijan and Manhaeve, Robin and Marra, Giuseppe},
  booktitle = {IJCAI},
  year      = {2020},
}

@article{chavira2008,
  title={On probabilistic inference by weighted model counting},
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  journal={Artificial Intelligence},
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  number={6-7},
  pages={772--799},
  year={2008},
  publisher={Elsevier}
}

@inproceedings{sang2005,
 author = {Sang, Tian and Bearne, Paul and Kautz, Henry},
 title = {Performing Bayesian Inference by Weighted Model Counting},
 booktitle = {AAAI},
 year = {2005}
}

@article{darwiche03,
 author = {Darwiche, Adnan},
 title = {A Differential Approach to Inference in Bayesian Networks},
 journal = {UAI},
 year = {2003},
}

@inproceedings{darwiche11,
 author = {Darwiche, Adnan},
 title = {SDD: A New Canonical Representation of Propositional Knowledge Bases},
 booktitle = {IJCAI},
 year = {2011}
}

@article{darwiche02,
  title={A knowledge compilation map},
  author={Darwiche, Adnan and Marquis, Pierre},
  journal={JAIR},
  year={2002}
}

@article{scudder1965probability,
  title={Probability of error of some adaptive pattern-recognition machines},
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  year={1965},
}

@article{mclachlan1975iterative,
  title={Iterative reclassification procedure for constructing an asymptotically optimal rule of allocation in discriminant analysis},
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}

@inproceedings{lee2013pseudo,
  title={Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks},
  booktitle={ICML Workshop on Challenges in Representation Learning},
  author={Lee, Dong-Hyun},
  year={2013}
}

@inproceedings{mcclosky2006effective,
  title={Effective self-training for parsing},
  author={McClosky, David and Charniak, Eugene and Johnson, Mark},
  booktitle={Proceedings of the main conference on human language technology conference of the North American Chapter of the Association of Computational Linguistics},
  year={2006},
  organization={Association for Computational Linguistics}
}

@inproceedings{rosenberg2005semi,
  title={Semi-supervised self-training of object detection models},
  author={Rosenberg, Chuck and Hebert, Martial and Schneiderman, Henry},
  year={2005},
  booktitle={Proceedings of the Seventh IEEE Workshops on Application of Computer Vision}
}

@article{xie2019self,
  title={Self-training with Noisy Student improves {ImageNet} classification},
  author={Qizhe Xie and Eduard Hovy and Minh-Thang Luong and Quoc V. Le},
  journal={arXiv preprint arXiv:1911.04252},
  year={2019}
}

@inproceedings{zou2018domain,
  title={Unsupervised domain adaptation for semantic segmentation via class-balanced self-training},
  author={Zou, Yang and Yu, Zhiding and Vijaya Kumar, BVK and Wang, Jinsong},
  booktitle={Proceedings of the European Conference on Computer Vision (ECCV)},
  pages={289--305},
  year={2018}
}

@article{arazo2019pseudo,
  title={Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning},
  author={Arazo, Eric and Ortego, Diego and Albert, Paul and O'Connor, Noel E. and McGuinness, Kevin},
  journal={arXiv preprint arXiv:1908.02983},
  year={2019}
}

@article{anonymous2019semi,
  title={Semi-supervised Learning by Coaching},
  author={Pham, Hieu and Le, Quoc V},
  journal={Submitted to the 8th International Conference on Learning Representations},
  note={\url{https://openreview.net/forum?id=rJe04p4YDB}},
  year={2019}
}

@article{miyato2018virtual,
  title={Virtual adversarial training: a regularization method for supervised and semi-supervised learning},
  author={Miyato, Takeru and Maeda, Shin-ichi and Ishii, Shin and Koyama, Masanori},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  year={2018},
}

@incollection{berthelot2019mixmatch,
title = {MixMatch: A Holistic Approach to Semi-Supervised Learning},
author = {Berthelot, David and Carlini, Nicholas and Goodfellow, Ian and Papernot, Nicolas and Oliver, Avital and Raffel, Colin A},
booktitle = {Advances in Neural Information Processing Systems 32},
year = {2019},
}

@inproceedings{kimmig2012short,
  title={A short introduction to probabilistic soft logic},
  author={Kimmig, Angelika and Bach, Stephen and Broecheler, Matthias and Huang, Bert and Getoor, Lise},
  booktitle={Proceedings of the NIPS Workshop on Probabilistic Programming: Foundations and Applications},
  year={2012}
}

@inproceedings{Choi2013dynamic,
author = {Choi, Arthur and Darwiche, Adnan},
title = {Dynamic Minimization of Sentential Decision Diagrams},
year = {2013},
publisher = {AAAI Press},
booktitle = {Proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence},
pages = {187–194},
numpages = {8},
location = {Bellevue, Washington},
series = {AAAI'13}
}

@inproceedings{Oztok2015topdown,
author = {Oztok, Umut and Darwiche, Adnan},
title = {A Top-down Compiler for Sentential Decision Diagrams},
year = {2015},
isbn = {9781577357384},
publisher = {AAAI Press},
abstract = {The sentential decision diagram (SDD) has been recently proposed as a new tractable representation of Boolean functions that generalizes the influential ordered binary decision diagram (OBDD). Empirically, compiling CNFs into SDDs has yielded significant improvements in both time and space over compiling them into OBDDs, using a bottom-up compilation approach. In this work, we present a top-down CNF to SDD compiler that is based on techniques from the SAT literature. We compare the presented compiler empirically to the state-of-the-art, bottom-up SDD compiler, showing orders-of-magnitude improvements in compilation time.},
booktitle = {Proceedings of the 24th International Conference on Artificial Intelligence},
pages = {3141–3148},
numpages = {8},
location = {Buenos Aires, Argentina},
series = {IJCAI'15}
}

@inproceedings{Darwiche2004advances,
author = {Darwiche, Adnan},
title = {New Advances in Compiling CNF to Decomposable Negation Normal Form},
year = {2004},
isbn = {9781586034528},
publisher = {IOS Press},
address = {NLD},
abstract = {We describe a new algorithm for compiling conjunctive normal form (CNF) into Deterministic Decomposable Negation Normal (d-DNNF), which is a tractable logical form that permits model counting in polynomial time. The new implementation is based on latest techniques from both the SAT and OBDD literatures, and appears to be orders of magnitude more efficient than previous algorithms for this purpose. We compare our compiler experimentally to state of the art model counters, OBDD compilers, and previous CNF2dDNNF compilers.},
booktitle = {Proceedings of the 16th European Conference on Artificial Intelligence},
pages = {318–322},
numpages = {5},
location = {Valencia, Spain},
series = {ECAI'04}
}

@inproceedings{Muise2012dsharp,
author = {Muise, Christian and McIlraith, Sheila A. and Beck, J. Christopher and Hsu, Eric I.},
title = {Dsharp: Fast d-DNNF Compilation with SharpSAT},
year = {2012},
isbn = {9783642303524},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
url = {https://doi.org/10.1007/978-3-642-30353-1_36},
doi = {10.1007/978-3-642-30353-1_36},
pages = {356–361},
numpages = {6},
location = {Toronto, ON, Canada},
series = {Canadian AI'12}
}

@inproceedings{Lagniez2017improveddnnf,
  author    = {Jean-Marie Lagniez and Pierre Marquis},
  title     = {An Improved Decision-DNNF Compiler},
  booktitle = {Proceedings of the Twenty-Sixth International Joint Conference on
               Artificial Intelligence, {IJCAI-17}},
  pages     = {667--673},
  year      = {2017},
  doi       = {10.24963/ijcai.2017/93},
  url       = {https://doi.org/10.24963/ijcai.2017/93},
}

@article{Takahisa2012implementing,
author = {Toda, Takahisa and Soh, Takehide},
title = {Implementing Efficient All Solutions SAT Solvers},
year = {2016},
issue_date = {2016},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {21},
issn = {1084-6654},
url = {https://doi.org/10.1145/2975585},
doi = {10.1145/2975585},
journal = {ACM J. Exp. Algorithmics},
month = {nov},
}

@inproceedings{Toussaint2009robot,
author = {Toussaint, Marc},
title = {Robot Trajectory Optimization Using Approximate Inference},
year = {2009},
isbn = {9781605585161},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
booktitle = {Proceedings of the 26th Annual International Conference on Machine Learning},
series = {ICML '09}
}

@incollection{Paszke19,
title = {PyTorch: An Imperative Style, High-Performance Deep Learning Library},
author = {Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Kopf, Andreas and Yang, Edward and DeVito, Zachary and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and Bai, Junjie and Chintala, Soumith},
booktitle = {Advances in Neural Information Processing Systems 32},
pages = {8024--8035},
year = {2019},
publisher = {Curran Associates, Inc.},
url = {https://proceedings.neurips.cc/paper/2019/file/bdbca288fee7f92f2bfa9f7012727740-Paper.pdf}
}