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Abstract

Neuro-Symbolic Artificial Intelligence – the combination of symbolic methods with methods that are based on artificial neural networks – has a long-standing history. In this article, we provide a structured overview of current trends, by means of categorizing recent publications from key conferences. The article is meant to serve as a convenient starting point for research on the general topic.

Keywords

Artificial neural networks deep learning knowledge representation and reasoning neuro-symbolic artificial intelligence

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References

A.M.

Alaa and

van der Schaar, Demystifying black-box models with symbolic metamodels, in: Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems, 2019, NeurIPS 2019, Vancouver, BC, Canada, December 8–14, 2019,

H.M.

Wallach,

Larochelle,

Beygelzimer,

d’Alché-Buc,

E.B.

Fox and

Garnett, eds, 2019, pp. 11301–11311, https://proceedings.neurips.cc/paper/2019/hash/567b8f5f423af15818a068235807edc0-Abstract.html .

Allamanis,

Chanthirasegaran,

Kohli and

Sutton, Learning continuous semantic representations of symbolic expressions, in: Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6–11 August 2017,

Precup and

Y.W.

Teh, eds, Proceedings of Machine Learning Research, Vol. 70, PMLR, 2017, pp. 80–88, http://proceedings.mlr.press/v70/allamanis17a.html .

Amizadeh,

Palangi,

Polozov,

Huang and

Koishida, Neuro-symbolic visual reasoning: Disentangling “visual” from “reasoning”, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 279–290, Virtual Event, http://proceedings.mlr.press/v119/amizadeh20a.html.

Arabshahi,

Singh and

Anandkumar, Combining symbolic expressions and black-box function evaluations in neural programs, in: 6th International Conference on Learning Representations, ICLR 2018, Conference Track Proceedings, Vancouver, BC, Canada, April 30–May 3, 2018, OpenReview.net, 2018, https://openreview.net/forum?id=Hksj2WWAW .

Asai and

Fukunaga, Classical planning in deep latent space: Bridging the subsymbolic-symbolic boundary, in: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI-18), the 30th Innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2–7, 2018,

S.A.

McIlraith and

K.Q.

Weinberger, eds, AAAI Press, 2018, pp. 6094–6101, https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16302 .

Asai and

Muise, Learning neural–symbolic descriptive planning models via cube-space priors: The voyage home (to STRIPS), in: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020,

Bessiere, ed., ijcai.org, 2020, pp. 2676–2682. doi:10.24963/ijcai.2020/371.

Bader and

Hitzler, Dimensions of neural–symbolic integration – a structured survey, in: We Will Show Them! Essays in Honour of Dov Gabbay, Volume One,

S.N.

Artëmov,

Barringer,

A.S.

d’Avila Garcez,

L.C.

Lamb and

Woods, eds, College Publications, 2005, pp. 167–194.

T.R.

Besold,

A.S.

d’Avila Garcez,

Bader,

Bowman,

P.M.

Domingos,

Hitzler,

Kühnberger,

L.C.

Lamb,

Lowd,

P.M.V.

Lima,

de Penning,

Pinkas,

Poon and

Zaverucha, Neural-symbolic learning and reasoning: A survey and interpretation, CoRR abs/1711.03902, 2017, http://arxiv.org/abs/1711.03902.

Bianchi and

Hitzler, On the capabilities of logic tensor networks for deductive reasoning, in: Proceedings of the AAAI 2019 Spring Symposium on Combining Machine Learning with Knowledge Engineering (AAAI-MAKE 2019), Stanford University, Palo Alto, California, USA, March 25–27, 2019,

Martin,

Hinkelmann,

Gerber,

Lenat,

van Harmelen and

Clark, eds, CEUR Workshop Proceedings, Vol. 2350, CEUR-WS.org, 2019, http://ceur-ws.org/Vol-2350/paper22.pdf .

10.

Cao,

Lu and

Xu, Deep neural networks for learning graph representations, in: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, Arizona, USA, February 12–17, 2016,

Schuurmans and

M.P.

Wellman, eds, AAAI Press, 2016, pp. 1145–1152, http://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/view/12423 .

11.

Charton,

Hayat and

Lample, Learning advanced mathematical computations from examples, in: 9th International Conference on Learning Representations, ICLR 2021, Austria, May 3–7, 2021, OpenReview.net, 2021, Virtual Event, https://openreview.net/forum?id=-gfhS00XfKj.

12.

Chen,

Bai,

Zhao,

Ament,

J.M.

Gregoire and

C.P.

Gomes, Deep reasoning networks for unsupervised pattern de-mixing with constraint reasoning, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 1500–1509, Virtual Event, http://proceedings.mlr.press/v119/chen20a.html.

13.

Chen,

Liang,

A.W.

Yu,

Song and

Zhou, Compositional generalization via neural–symbolic stack machines, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/12b1e42dc0746f22cf361267de07073f-Abstract.html.

14.

Chen,

Liang,

A.W.

Yu,

Zhou,

Song and

Q.V.

Le, Neural symbolic reader: Scalable integration of distributed and symbolic representations for reading comprehension, in: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26–30, 2020, OpenReview.net, 2020, https://openreview.net/forum?id=ryxjnREFwH .

15.

Chen and

Tian, Learning to perform local rewriting for combinatorial optimization, in: Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems, 2019, NeurIPS 2019, Vancouver, BC, Canada, December 8–14, 2019,

H.M.

Wallach,

Larochelle,

Beygelzimer,

d’Alché-Buc,

E.B.

Fox and

Garnett, eds, 2019, pp. 6278–6289, https://proceedings.neurips.cc/paper/2019/hash/131f383b434fdf48079bff1e44e2d9a5-Abstract.html .

16.

F.C.

Chua and

N.P.

Duffy, DeepCPCFG: Deep learning and context free grammars for end-to-end information extraction, CoRR abs/2103.05908, 2021, https://arxiv.org/abs/2103.05908.

17.

W.W.

Cohen,

Sun,

R.A.

Hofer and

Siegler, Scalable neural methods for reasoning with a symbolic knowledge base, in: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26–30, 2020, OpenReview.net, 2020, https://openreview.net/forum?id=BJlguT4YPr .

18.

Craandijk and

Bex, Deep learning for abstract argumentation semantics, in: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020,

Bessiere, ed., ijcai.org, 2020, pp. 1667–1673. doi:10.24963/ijcai.2020/231.

19.

M.D.

Cranmer,

Sanchez-Gonzalez,

P.W.

Battaglia,

Xu,

Cranmer,

D.N.

Spergel and

Ho, Discovering symbolic models from deep learning with inductive biases, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems, 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/c9f2f917078bd2db12f23c3b413d9cba-Abstract.html.

20.

Dang-Nhu, PLANS: Neuro-symbolic program learning from videos, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/fe131d7f5a6b38b23cc967316c13dae2-Abstract.html.

21.

A.S.

d’Avila Garcez,

L.C.

Lamb and

D.M.

Gabbay, Neural-Symbolic Cognitive Reasoning, Cognitive Technologies, Springer, 2009. ISBN 978-3-540-73245-7. doi:10.1007/978-3-540-73246-4.

22.

de Penning,

A.S.

d’Avila Garcez,

L.C.

Lamb and

J.C.

Meyer, A neural–symbolic cognitive agent for online learning and reasoning, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011,

Walsh, ed., IJCAI/AAAI, 2011, pp. 1653–1658. doi:10.5591/978-1-57735-516-8/IJCAI11-278.

23.

Demeter and

Downey, Just add functions: A neural–symbolic language model, in: The Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, The Thirty-Second Innovative Applications of Artificial Intelligence Conference, IAAI 2020, The Tenth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2020, New York, NY, USA, February 7–12, 2020, AAAI Press, 2020, pp. 7634–7642, https://aaai.org/ojs/index.php/AAAI/article/view/6264 .

24.

Deng,

Zhang,

Chen,

J.Z.

Pan and

Chen, Knowledge-driven stock trend prediction and explanation via temporal convolutional network, in: Companion of the 2019 World Wide Web Conference, WWW 2019, San Francisco, CA, USA, May 13–17, 2019,

Amer-Yahia,

Mahdian,

Goel,

Houben,

Lerman,

J.J.

McAuley,

Baeza-Yates and

Zia, eds, ACM, 2019, pp. 678–685. doi:10.1145/3308560.3317701.

25.

Dhamo,

Farshad,

Laina,

Navab,

G.D.

Hager,

Tombari and

Rupprecht, Semantic image manipulation using scene graphs, in: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13–19, 2020, IEEE, 2020, pp. 5212–5221. doi:10.1109/CVPR42600.2020.00526.

26.

Dhingra,

Zaheer,

Balachandran,

Neubig,

Salakhutdinov and

W.W.

Cohen, Differentiable reasoning over a virtual knowledge base, in: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26–30, 2020, OpenReview.net, 2020, https://openreview.net/forum?id=SJxstlHFPH.

27.

Donadello,

Serafini and

A.S.

d’Avila Garcez, Logic tensor networks for semantic image interpretation, in: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19–25, 2017,

Sierra, ed., ijcai.org, 2017, pp. 1596–1602. doi:10.24963/ijcai.2017/221.

28.

Eberhart,

Ebrahimi,

Zhou,

Shimizu and

Hitzler, Completion reasoning emulation for the description logic EL+, in: Proceedings of the AAAI 2020 Spring Symposium on Combining Machine Learning and Knowledge Engineering in Practice, AAAI-MAKE 2020, Volume I, Palo Alto, CA, USA, March 23–25, 2020,

Martin,

Hinkelmann,

Fill,

Gerber,

Lenat,

Stolle and

van Harmelen, eds, CEUR Workshop Proceedings, Vol. 2600, CEUR-WS.org, 2020, http://ceur-ws.org/Vol-2600/paper5.pdf .

29.

Ebrahimi,

Eberhart,

Bianchi and

Hitzler, Towards bridging the neuro-symbolic gap: Deep deductive reasoners, Applied Intelligence 51(9) (2021), 6326–6348. doi:10.1007/s10489-020-02165-6.

30.

Ebrahimi,

Eberhart and

Hitzler, On the capabilities of pointer networks for deep deductive reasoning, CoRR abs/2106.09225, 2021, https://arxiv.org/abs/2106.09225.

31.

Ebrahimi,

M.K.

Sarker,

Bianchi,

Xie,

Eberhart,

Doran,

Kim and

Hitzler, Neuro-symbolic deductive reasoning for cross-knowledge graph entailment, in: Proceedings of the AAAI 2021 Spring Symposium on Combining Machine Learning and Knowledge Engineering (AAAI-MAKE 2021), Stanford University, Palo Alto, California, USA, March 22–24, 2021,

Martin,

Hinkelmann,

Fill,

Gerber,

Lenat,

Stolle and

van Harmelen, eds, CEUR Workshop Proceedings, Vol. 2846, CEUR-WS.org, 2021, http://ceur-ws.org/Vol-2846/paper8.pdf .

32.

Fischer,

Balunovic,

Drachsler-Cohen,

Gehr,

Zhang and

M.T.

Vechev, DL2: Training and querying neural networks with logic, in: Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, California, USA, 9–15 June 2019,

Chaudhuri and

Salakhutdinov, eds, Proceedings of Machine Learning Research, Vol. 97, PMLR, 2019, pp. 1931–1941, http://proceedings.mlr.press/v97/fischer19a.html .

33.

Garg,

Bajpai and Mausam , Symbolic network: Generalized neural policies for relational MDPs, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 3397–3407, Virtual Event, http://proceedings.mlr.press/v119/garg20a.html.

34.

Hammer and

Hitzler (eds), Perspectives of Neural-Symbolic Integration, Studies in Computational Intelligence, Vol. 77, Springer, 2007. ISBN 978-3-540-73953-1.

35.

Hitzler, A review of the semantic web field, Commun. ACM 64(2) (2021), 76–83. doi:10.1145/3397512.

36.

Hitzler,

Bianchi,

Ebrahimi and

M.K.

Sarker, Neural-symbolic integration and the semantic web, Semantic Web 11(1) (2020), 3–11. doi:10.3233/SW-190368.

37.

Hitzler,

Hölldobler and

A.K.

Seda, Logic programs and connectionist networks, J. Appl. Log. 2(3) (2004), 245–272. doi:10.1016/j.jal.2004.03.002.

38.

Hitzler,

Krötzsch and

Rudolph, Foundations of Semantic Web Technologies, Chapman and Hall/CRC Press, 2010, http://www.semantic-web-book.org/ . ISBN 9781420090505.

39.

Hohenecker and

Lukasiewicz, Ontology reasoning with deep neural networks, J. Artif. Intell. Res. 68 (2020), 503–540. doi:10.1613/jair.1.11661.

40.

Hu,

Andreas,

Rohrbach,

Darrell and

Saenko, Learning to reason: End-to-end module networks for visual question answering, in: IEEE International Conference on Computer Vision, ICCV 2017, Venice, Italy, October 22–29, 2017, IEEE Computer Society, 2017, pp. 804–813. doi:10.1109/ICCV.2017.93.

41.

Hu,

Ma,

Liu,

E.H.

Hovy and

E.P.

Xing, Harnessing deep neural networks with logic rules, in: Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, Volume 1: Long Papers, Berlin, Germany, August 7–12, 2016, The Association for Computer Linguistics, 2016. doi:10.18653/v1/p16-1228.

42.

Jiang and

Ahn, Generative neurosymbolic machines, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/94c28dcfc97557df0df6d1f7222fc384-Abstract.html.

43.

Jiang and

Luo, Neural logic reinforcement learning, in: Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, California, USA, 9–15 June 2019,

Chaudhuri and

Salakhutdinov, eds, Proceedings of Machine Learning Research, Vol. 97, PMLR, 2019, pp. 3110–3119, http://proceedings.mlr.press/v97/jiang19a.html .

44.

Lample and

Charton, Deep learning for symbolic mathematics, in: 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26–30, 2020, OpenReview.net, 2020, https://openreview.net/forum?id=S1eZYeHFDS .

45.

Li,

Huang,

Hong,

Chen,

Y.N.

Wu and

Zhu, Closed loop neural–symbolic learning via integrating neural perception, grammar parsing, and symbolic reasoning, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 5884–5894, Virtual Event, http://proceedings.mlr.press/v119/li20f.html.

46.

Liang,

Berant,

Q.V.

Le,

K.D.

Forbus and

Lao, Neural symbolic machines: Learning semantic parsers on freebase with weak supervision, in: Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics, ACL 2017, Volume 1: Long Papers, Vancouver, Canada, July 30–August 4,

Barzilay and

Kan, eds, Association for Computational Linguistics, 2017, pp. 23–33. doi:10.18653/v1/P17-1003.

47.

Liang,

Hu,

Zhang,

Lin and

E.P.

Xing, Symbolic graph reasoning meets convolutions, in: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems, 2018, NeurIPS 2018, Montréal, Canada, December 3–8, 2018,

Bengio,

H.M.

Wallach,

Larochelle,

Grauman,

Cesa-Bianchi and

Garnett, eds, 2018, pp. 1858–1868, https://proceedings.neurips.cc/paper/2018/hash/cbb6a3b884f4f88b3a8e3d44c636cbd8-Abstract.html .

48.

Lyu,

Yang,

Liu and

Gustafson, SDRL: Interpretable and data-efficient deep reinforcement learning leveraging symbolic planning, in: The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019, Honolulu, Hawaii, USA, January 27–February 1, 2019, AAAI Press, 2019, pp. 2970–2977. doi:10.1609/aaai.v33i01.33012970.

49.

Makni and

J.A.

Hendler, Deep learning for noise-tolerant RDFS reasoning, Semantic Web 10(5) (2019), 823–862. doi:10.3233/SW-190363.

50.

Manhaeve,

Dumancic,

Kimmig,

Demeester and

L.D.

Raedt, DeepProbLog: Neural probabilistic logic programming, in: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems, 2018, NeurIPS 2018, Montréal, Canada, December 3–8, 2018,

Bengio,

H.M.

Wallach,

Larochelle,

Grauman,

Cesa-Bianchi and

Garnett, eds, 2018, pp. 3753–3763, https://proceedings.neurips.cc/paper/2018/hash/dc5d637ed5e62c36ecb73b654b05ba2a-Abstract.html .

51.

Mao,

Gan,

Kohli,

J.B.

Tenenbaum and

Wu, The neuro-symbolic concept learner: Interpreting scenes, words, and sentences from natural supervision, in: 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6–9, 2019, OpenReview.net, 2019, https://openreview.net/forum?id=rJgMlhRctm.

52.

McCarthy, Epistomological challenges for connectionism, Behavioral and Brain Sciences 11 (1988), 44. doi:10.1017/S0140525X0005264X.

53.

W.S.

McCulloch and

Pitts, A logical calculus of the ideas immanent in nervous activity, Bulletin of Mathematical Biophysics 5 (1943), 115–133. doi:10.1007/BF02478259.

54.

Minervini,

Riedel,

Stenetorp,

Grefenstette and

Rocktäschel, Learning reasoning strategies in end-to-end differentiable proving, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 6938–6949, Virtual Event, http://proceedings.mlr.press/v119/minervini20a.html.

55.

Mou,

Lu,

Li and

Jin, Coupling distributed and symbolic execution for natural language queries, in: Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6–11 August 2017,

Precup and

Y.W.

Teh, eds, Proceedings of Machine Learning Research, Vol. 70, PMLR, 2017, pp. 2518–2526, http://proceedings.mlr.press/v70/mou17a.html .

56.

Niepert,

Ahmed and

Kutzkov, Learning convolutional neural networks for graphs, in: Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19–24, 2016,

Balcan and

K.Q.

Weinberger, eds, JMLR Workshop and Conference Proceedings, Vol. 48, JMLR.org, 2016, pp. 2014–2023, http://proceedings.mlr.press/v48/niepert16.html .

57.

Parisotto,

Mohamed,

Singh,

Li,

Zhou and

Kohli, Neuro-symbolic program synthesis, in: 5th International Conference on Learning Representations, ICLR 2017, Conference Track Proceedings, Toulon, France, April 24–26, 2017, OpenReview.net, 2017, https://openreview.net/forum?id=rJ0JwFcex .

58.

Santoro,

Hill,

D.G.T.

Barrett,

A.S.

Morcos and

T.P.

Lillicrap, Measuring abstract reasoning in neural networks, in: Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, July 10–15, 2018,

J.G.

Dy and

Krause, eds, Proceedings of Machine Learning Research, Vol. 80, PMLR, 2018, pp. 4477–4486, http://proceedings.mlr.press/v80/santoro18a.html .

59.

M.K.

Sarker,

Schwartz,

Hitzler,

Zhou,

Nadella,

B.S.

Minnery,

Juvina,

M.L.

Raymer and

W.R.

Aue, Wikipedia knowledge graph for explainable AI, in: Knowledge Graphs and Semantic Web – Second Iberoamerican Conference and First Indo-American Conference, KGSWC 2020, Proceedings, Mérida, Mexico, November 26–27, 2020,

Villazón-Terrazas,

Ortiz-Rodríguez,

S.M.

Tiwari and

S.K.

Shandilya, eds, Communications in Computer and Information Science, Vol. 1232, Springer, 2020, pp. 72–87. doi:10.1007/978-3-030-65384-2_6.

60.

M.K.

Sarker,

Xie,

Doran,

M.L.

Raymer and

Hitzler, Explaining trained neural networks with semantic web technologies: First steps, in: Proceedings of the Twelfth International Workshop on Neural-Symbolic Learning and Reasoning, NeSy 2017, London, UK, July 17–18, 2017,

T.R.

Besold,

A.S.

d’Avila Garcez and

Noble, eds, CEUR Workshop Proceedings, Vol. 2003, CEUR-WS.org, 2017, http://ceur-ws.org/Vol-2003/NeSy17_paper4.pdf .

61.

R.R.

Selvaraju,

Chattopadhyay,

Elhoseiny,

Sharma,

Batra,

Parikh and

Lee, Choose your neuron: Incorporating domain knowledge through neuron-importance, in: Computer Vision – ECCV 2018 – 15th European Conference, Proceedings, Part XIII, Munich, Germany, September 8–14, 2018,

Ferrari,

Hebert,

Sminchisescu and

Weiss, eds, Lecture Notes in Computer Science, Vol. 11217, Springer, 2018, pp. 540–556. doi:10.1007/978-3-030-01261-8_32.

62.

Shastri, Advances in SHRUTI – a neurally motivated model of relational knowledge representation and rapid inference using temporal synchrony, Appl. Intell. 11(1) (1999), 79–108. doi:10.1023/A:1008380614985.

63.

K.K.

Teru,

Denis and

Hamilton, Inductive relation prediction by subgraph reasoning, in: Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13–18 July 2020, Proceedings of Machine Learning Research, Vol. 119, PMLR, 2020, pp. 9448–9457, Virtual Event, http://proceedings.mlr.press/v119/teru20a.html.

64.

Trivedi,

Dai,

Wang and

Song, Know-evolve: Deep temporal reasoning for dynamic knowledge graphs, in: Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6–11 August 2017,

Precup and

Y.W.

Teh, eds, Proceedings of Machine Learning Research, Vol. 70, PMLR, 2017, pp. 3462–3471, http://proceedings.mlr.press/v70/trivedi17a.html .

65.

van Harmelen and

ten Teije, A boxology of design patterns for hybrid learning and reasoning systems, J. Web Eng. 18(1–3) (2019), 97–124. doi:10.13052/jwe1540-9589.18133.

66.

Vedantam,

Desai,

Lee,

Rohrbach,

Batra and

Parikh, Probabilistic neural symbolic models for interpretable visual question answering, in: Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, California, USA, 9–15 June 2019,

Chaudhuri and

Salakhutdinov, eds, Proceedings of Machine Learning Research, Vol. 97, PMLR, 2019, pp. 6428–6437, http://proceedings.mlr.press/v97/vedantam19a.html .

67.

Velickovic,

Buesing,

M.C.

Overlan,

Pascanu,

Vinyals and

Blundell, Pointer graph networks, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/176bf6219855a6eb1f3a30903e34b6fb-Abstract.html.

68.

Vinyals,

Fortunato and

Jaitly, Pointer networks, in: Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems, 2015, Montreal, Quebec, Canada, December 7–12, 2015,

Cortes,

N.D.

Lawrence,

D.D.

Lee,

Sugiyama and

Garnett, eds, 2015, pp. 2692–2700, https://proceedings.neurips.cc/paper/2015/hash/29921001f2f04bd3baee84a12e98098f-Abstract.html .

69.

Wang,

P.L.

Donti,

Wilder and

J.Z.

Kolter, SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver, in: Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, California, USA, 9–15 June 2019,

Chaudhuri and

Salakhutdinov, eds, Proceedings of Machine Learning Research, Vol. 97, PMLR, 2019, pp. 6545–6554, http://proceedings.mlr.press/v97/wang19e.html .

70.

Xiao,

Dymetman and

Gardent, Symbolic priors for RNN-based semantic parsing, in: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19–25, 2017,

Sierra, ed., ijcai.org, 2017, pp. 4186–4192. doi:10.24963/ijcai.2017/585.

71.

Xie,

Xu,

K.S.

Meel,

M.S.

Kankanhalli and

Soh, Embedding symbolic knowledge into deep networks, in: Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems, 2019, NeurIPS 2019, Vancouver, BC, Canada, December 8–14, 2019,

H.M.

Wallach,

Larochelle,

Beygelzimer,

d’Alché-Buc,

E.B.

Fox and

Garnett, eds, 2019, pp. 4235–4245, https://proceedings.neurips.cc/paper/2019/hash/7b66b4fd401a271a1c7224027ce111bc-Abstract.html .

72.

Xiong,

Merity and

Socher, Dynamic memory networks for visual and textual question answering, in: Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19–24, 2016,

Balcan and

K.Q.

Weinberger, eds, JMLR Workshop and Conference Proceedings, Vol. 48, JMLR.org, 2016, pp. 2397–2406, http://proceedings.mlr.press/v48/xiong16.html .

73.

Xu,

Zhang,

Friedman,

Liang and

G.V.

den Broeck, A semantic loss function for deep learning with symbolic knowledge, in: Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, July 10–15, 2018,

J.G.

Dy and

Krause, eds, Proceedings of Machine Learning Research, Vol. 80, PMLR, 2018, pp. 5498–5507, http://proceedings.mlr.press/v80/xu18h.html .

74.

Yang,

Lyu,

Liu and

Gustafson, PEORL: Integrating symbolic planning and hierarchical reinforcement learning for robust decision-making, in: Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, Stockholm, July 13–19, 2018,

Lang, ed., ijcai.org, 2018, pp. 4860–4866. doi:10.24963/ijcai.2018/675.

75.

Yeh,

Kim,

S.Ö.

Arik,

Li,

Pfister and

Ravikumar, On completeness-aware concept-based explanations in deep neural networks, in: Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6–12, 2020,

Larochelle,

Ranzato,

Hadsell,

Balcan and

Lin, eds, 2020, virtual, https://proceedings.neurips.cc/paper/2020/hash/ecb287ff763c169694f682af52c1f309-Abstract.html.

76.

Yi,

Wu,

Gan,

Torralba,

Kohli and

Tenenbaum, Neural-symbolic VQA: Disentangling reasoning from vision and language understanding, in: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems, 2018, NeurIPS 2018, Montréal, Canada, December 3–8, 2018,

Bengio,

H.M.

Wallach,

Larochelle,

Grauman,

Cesa-Bianchi and

Garnett, eds, 2018, pp. 1039–1050, https://proceedings.neurips.cc/paper/2018/hash/5e388103a391daabe3de1d76a6739ccd-Abstract.html .

77.

Yildirim,

Gerstenberg,

Saeed,

Toussaint and

Tenenbaum, Physical problem solving: Joint planning with symbolic, geometric, and dynamic constraints, in: Proceedings of the 39th Annual Meeting of the Cognitive Science Society, CogSci 2017, London, UK, 16–29 July 2017,

Gunzelmann,

Howes,

Tenbrink and

E.J.

Davelaar, eds, cognitivesciencesociety.org, 2017, https://mindmodeling.org/cogsci2017/papers/0676/index.html .

78.

Young,

Bastani and

Naik, Learning neurosymbolic generative models via program synthesis, in: Proceedings of the 36th International Conference on Machine Learning, ICML 2019, Long Beach, California, USA, 9–15 June 2019,

Chaudhuri and

Salakhutdinov, eds, Proceedings of Machine Learning Research, Vol. 97, PMLR, 2019, pp. 7144–7153, http://proceedings.mlr.press/v97/young19a.html .

79.

Zhang,

Solar-Lezama and

Singh, Interpreting neural network judgments via minimal, stable, and symbolic corrections, in: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems, 2018, NeurIPS 2018, Montréal, Canada, December 3–8, 2018,

Bengio,

H.M.

Wallach,

Larochelle,

Grauman,

Cesa-Bianchi and

Garnett, eds, 2018, pp. 4879–4890, https://proceedings.neurips.cc/paper/2018/hash/300891a62162b960cf02ce3827bb363c-Abstract.html .

80.

Zhou,

Bau,

Oliva and

Torralba, Interpreting deep visual representations via network dissection, IEEE Trans. Pattern Anal. Mach. Intell. 41(9) (2019), 2131–2145. doi:10.1109/TPAMI.2018.2858759.

Neuro-symbolic artificial intelligence

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