{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T01:54:20Z","timestamp":1778637260153,"version":"3.51.4"},"publisher-location":"New York, NY, USA","reference-count":39,"publisher":"ACM","license":[{"start":{"date-parts":[[2020,6,11]],"date-time":"2020-06-11T00:00:00Z","timestamp":1591833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100014718","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-18-42456, CNS-18-01426, CNS-16-17670, CCF-1918400"],"award-info":[{"award-number":["CNS-18-42456, CNS-18-01426, CNS-16-17670, CCF-1918400"]}],"id":[{"id":"10.13039\/100014718","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100015089","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-17-1-2010"],"award-info":[{"award-number":["N00014-17-1-2010"]}],"id":[{"id":"10.13039\/100015089","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,6,11]]},"DOI":"10.1145\/3385412.3385986","type":"proceedings-article","created":{"date-parts":[[2020,6,7]],"date-time":"2020-06-07T01:40:10Z","timestamp":1591494010000},"page":"106-120","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":36,"title":["Learning nonlinear loop invariants with gated continuous logic networks"],"prefix":"10.1145","author":[{"given":"Jianan","family":"Yao","sequence":"first","affiliation":[{"name":"Columbia University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriel","family":"Ryan","sequence":"additional","affiliation":[{"name":"Columbia University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justin","family":"Wong","sequence":"additional","affiliation":[{"name":"Columbia University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suman","family":"Jana","sequence":"additional","affiliation":[{"name":"Columbia University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronghui","family":"Gu","sequence":"additional","affiliation":[{"name":"Columbia University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2020,6,11]]},"reference":[{"key":"e_1_3_2_1_1_1","volume-title":"Learning To Solve Circuit-SAT: An Unsupervised Differentiable Approach. In International Conference on Learning Representations. https: \/\/openreview.net\/forum?id=BJxgz2R9t7","author":"Amizadeh Saeed","year":"2019","unstructured":"Saeed Amizadeh, Sergiy Matusevych, and Markus Weimer. 2019. Learning To Solve Circuit-SAT: An Unsupervised Differentiable Approach. In International Conference on Learning Representations. https: \/\/openreview.net\/forum?id=BJxgz2R9t7"},{"key":"e_1_3_2_1_2_1","volume-title":"Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473","author":"Bahdanau Dzmitry","year":"2014","unstructured":"Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2014. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473 (2014)."},{"key":"e_1_3_2_1_3_1","unstructured":"Mislav Balunovic Pavol Bielik and Martin Vechev. 2018. Learning to solve SMT formulas. In Advances in Neural Information Processing Systems. 10317\u201310328."},{"key":"e_1_3_2_1_4_1","unstructured":"A. Biere H. van Maaren and T. Walsh. 2009. Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications. IOS Press Amsterdam The Netherlands The Netherlands."},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/371282.371285"},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11562948_10"},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/1792734.1792766"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1613\/jair.5714"},{"key":"e_1_3_2_1_9_1","volume-title":"Compositional recurrence analysis. In 2015 Formal Methods in Computer-Aided Design (FMCAD)","author":"Farzan Azadeh","unstructured":"Azadeh Farzan and Zachary Kincaid. 2015. Compositional recurrence analysis. In 2015 Formal Methods in Computer-Aided Design (FMCAD). IEEE, 57\u201364."},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2506375"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08867-9_5"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/2837614.2837664"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"crossref","unstructured":"Felix A Gers J\u00fcrgen Schmidhuber and Fred Cummins. 1999. Learning to forget: Continual prediction with LSTM. (1999).","DOI":"10.1049\/cp:19991218"},{"key":"e_1_3_2_1_14_1","volume-title":"Metamathematics of fuzzy logic","author":"H\u00e1jek Petr","unstructured":"Petr H\u00e1jek. 2013. Metamathematics of fuzzy logic. Vol. 4. Springer Science & Business Media."},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/363235.363259"},{"key":"e_1_3_2_1_16_1","volume-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167","author":"Ioffe Sergey","year":"2015","unstructured":"Sergey Ioffe and Christian Szegedy. 2015. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167 (2015)."},{"key":"e_1_3_2_1_17_1","volume-title":"Proceedings of the NIPS Workshop on Probabilistic Programming: Foundations and Applications. 1\u20134.","author":"Kimmig Angelika","year":"2012","unstructured":"Angelika Kimmig, Stephen Bach, Matthias Broecheler, Bert Huang, and Lise Getoor. 2012. A short introduction to probabilistic soft logic. In Proceedings of the NIPS Workshop on Probabilistic Programming: Foundations and Applications. 1\u20134."},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3140587.3062373"},{"key":"e_1_3_2_1_19_1","volume-title":"Proceedings of the ACM on Programming Languages 2, POPL","author":"Kincaid Zachary","year":"2017","unstructured":"Zachary Kincaid, John Cyphert, Jason Breck, and Thomas Reps. 2017. Non-linear reasoning for invariant synthesis. Proceedings of the ACM on Programming Languages 2, POPL (2017), 1\u201333."},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"crossref","unstructured":"Hai Lin Panos J Antsaklis et al. 2014. Hybrid dynamical systems: An introduction to control and verification. Foundations and Trends\u00ae in Systems and Control 1 1 (2014) 1\u2013172.","DOI":"10.1561\/2600000001"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3106237.3106281"},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.5555\/2337223.2337304"},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.5555\/2337223.2337304"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2556782"},{"key":"e_1_3_2_1_25_1","volume-title":"Millstein","author":"Padhi Saswat","year":"2017","unstructured":"Saswat Padhi and Todd D. Millstein. 2017. Data-Driven Loop Invariant Inference with Automatic Feature Synthesis. CoRR abs\/1707.02029 (2017). arXiv: 1707.02029 http:\/\/arxiv.org\/abs\/1707.02029"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980983.2908099"},{"key":"e_1_3_2_1_27_1","volume-title":"Inductive Logic Programming via Differentiable Deep Neural Logic Networks. arXiv preprint arXiv:1906.03523","author":"Payani Ali","year":"2019","unstructured":"Ali Payani and Faramarz Fekri. 2019. Inductive Logic Programming via Differentiable Deep Neural Logic Networks. arXiv preprint arXiv:1906.03523 (2019)."},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/1005285.1005324"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2007.01.002"},{"key":"e_1_3_2_1_30_1","volume-title":"International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=HJlfuTEtvB","author":"Ryan Gabriel","year":"2020","unstructured":"Gabriel Ryan, Justin Wong, Jianan Yao, Ronghui Gu, and Suman Jana. 2020. CLN2INV: Learning Loop Invariants with Continuous Logic Networks. In International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=HJlfuTEtvB"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-24258-9_24"},{"key":"e_1_3_2_1_32_1","volume-title":"International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=HJMC_iA5tm","author":"Selsam Daniel","unstructured":"Daniel Selsam, Matthew Lamm, Benedikt B\u00fcnz, Percy Liang, Leonardo de Moura, and David L. Dill. 2019. Learning a SAT Solver from Single-Bit Supervision. In International Conference on Learning Representations. https:\/\/openreview.net\/forum?id=HJMC_iA5tm"},{"key":"e_1_3_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-37036-6_31"},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-38856-9_21"},{"key":"e_1_3_2_1_35_1","unstructured":"Xujie Si Hanjun Dai Mukund Raghothaman Mayur Naik and Le Song. 2018. Learning loop invariants for program verification. In Advances in Neural Information Processing Systems. 7751\u20137762."},{"key":"e_1_3_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2019\/847"},{"key":"e_1_3_2_1_37_1","volume-title":"Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research 15, 1","author":"Srivastava Nitish","year":"2014","unstructured":"Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. 2014. Dropout: a simple way to prevent neural networks from overfitting. The journal of machine learning research 15, 1 (2014), 1929\u20131958."},{"key":"e_1_3_2_1_38_1","unstructured":"Fan Yang Zhilin Yang and William W Cohen. 2017. Differentiable learning of logical rules for knowledge base reasoning. In Advances in Neural Information Processing Systems. 2319\u20132328."},{"key":"e_1_3_2_1_39_1","volume-title":"June 15\u201320","author":"Yao Jianan","year":"2020","unstructured":"Jianan Yao, Gabriel Ryan, Justin Wong, Suman Jana, and Ronghui Gu. 2020. Learning Nonlinear Loop Invariants with Gated Continuous Logic Networks. arXiv: arXiv:2003.07959 Learning Nonlinear Loop Invariants with G-CLNs PLDI \u201920, June 15\u201320, 2020, London, UK"}],"event":{"name":"PLDI '20: 41st ACM SIGPLAN International Conference on Programming Language Design and Implementation","location":"London UK","acronym":"PLDI '20","sponsor":["SIGPLAN ACM Special Interest Group on Programming Languages"]},"container-title":["Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3385412.3385986","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3385412.3385986","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3385412.3385986","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:41:14Z","timestamp":1750200074000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3385412.3385986"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,11]]},"references-count":39,"alternative-id":["10.1145\/3385412.3385986","10.1145\/3385412"],"URL":"https:\/\/doi.org\/10.1145\/3385412.3385986","relation":{},"subject":[],"published":{"date-parts":[[2020,6,11]]},"assertion":[{"value":"2020-06-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}