DeepMath - Deep sequence models for premise selection

Advances in Neural Information Processing Systems

Volumn , Issue , 2016, Pages 2243-2251

  Alemi, Alexander A ^a   Chollet, François ^a   Een, Niklas ^a   Irving, Geoffrey ^a   Szegedy, Christian ^a   Urban, Josef ^b  

^a GOOGLE   (United Kingdom)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATED THEOREM PROVING; SEQUENCE MODELS; STATE OF THE ART; TWO STAGE APPROACH;

THEOREM PROVING;

EID: 85018904820     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (38)

1. M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. Software available from tensorflow.org.
2. G. Bancerek and P. Rudnicki. A Compendium of Continuous Lattices in MIZAR. J. Autom. Reasoning, 29(3-4):189-224, 2002.
3. P. Baudiš, J. Pichl, T. Vyskočil, and J. Šedivý. Sentence pair scoring: Towards unified framework for text comprehension. arXiv preprint arXiv:1603.06127, 2016.
4. J. C. Blanchette, C. Kaliszyk, L. C. Paulson, and J. Urban. Hammering towards QED. J. Formalized Reasoning, 9(1):101-148, 2016.
5. F. Chollet. Keras. https://github.com/fchollet/keras, 2015.
6. J. Chung, C. Gulcehre, K. Cho, and Y. Bengio. Gated feedback recurrent neural networks. arXiv preprint arXiv:1502.02367, 2015.
7. The Coq Proof Assistant. http://coq.inria.fr.
8. A. M. Dai and Q. V. Le. Semi-supervised sequence learning. In Advances in Neural Information Processing Systems, pages 3061-3069, 2015.
9. N. de Bruijn. The mathematical language AUTOMATH, its usage, and some of its extensions. In M. Laudet, editor, Proceedings of the Symposium on Automatic Demonstration, pages 29-61, Versailles, France, Dec. 1968. Springer-Verlag LNM 125.
10. X. Glorot and Y. Bengio. Understanding the difficulty of training deep feedforward neural networks. In International conference on artificial intelligence and statistics, pages 249-256, 2010.
11. G. Gonthier. The four colour theorem: Engineering of a formal proof. In D. Kapur, editor, Computer Mathematics, 8th Asian Symposium, ASCM 2007, Singapore, December 15-17, 2007. Revised and Invited Papers, Volume 5081 of Lecture Notes in Computer Science, page 333. Springer, 2007.
12. G. Gonthier, A. Asperti, J. Avigad, Y. Bertot, C. Cohen, F. Garillot, S. L. Roux, A. Mahboubi, R. O'Connor, S. O. Biha, I. Pasca, L. Rideau, A. Solovyev, E. Tassi, and L. Théry. A machine-checked proof of the Odd Order Theorem. In S. Blazy, C. Paulin-Mohring, and D. Pichardie, editors, ITP, Volume 7998 of LNCS, pages 163-179. Springer, 2013.
13. A. Grabowski, A. Korniłowicz, and A. Naumowicz. Mizar in a nutshell. J. Formalized Reasoning, 3(2):153-245, 2010.
14. T. C. Hales, M. Adams, G. Bauer, D. T. Dang, J. Harrison, T. L. Hoang, C. Kaliszyk, V. Magron, S. McLaughlin, T. T. Nguyen, T. Q. Nguyen, T. Nipkow, S. Obua, J. Pleso, J. Rute, A. Solovyev, A. H. T. Ta, T. N. Tran, D. T. Trieu, J. Urban, K. K. Vu, and R. Zumkeller. A formal proof of the Kepler conjecture. CoRR, abs/1501.02155, 2015.
15. J. Harrison. HOL Light: A tutorial introduction. In M. K. Srivas and A. J. Camilleri, editors, FMCAD, Volume 1166 of LNCS, pages 265-269. Springer, 1996.
16. J. Harrison, J. Urban, and F. Wiedijk. History of interactive theorem proving. In J. H. Siekmann, editor, Computational Logic, Volume 9 of Handbook of the History of Logic, pages 135-214. North-Holland, 2014.
17. S. Hochreiter and J. Schmidhuber. Long short-term memory. Neural computation, 9(8):1735-1780, 1997.
18. Ł. Kaiser and I. Sutskever. Neural gpus learn algorithms. arXiv preprint arXiv:1511.08228, 2015.
19. C. Kaliszyk and J. Urban. Stronger automation for Flyspeck by feature weighting and strategy evolution. In J. C. Blanchette and J. Urban, editors, PxTP 2013, Volume 14 of EPiC Series, pages 87-95. EasyChair, 2013.
20. C. Kaliszyk and J. Urban. Learning-assisted automated reasoning with Flyspeck. J. Autom. Reasoning, 53(2):173-213, 2014.
21. C. Kaliszyk and J. Urban. MizAR 40 for Mizar 40. J. Autom. Reasoning, 55(3):245-256, 2015.
22. C. Kaliszyk, J. Urban, and J. Vyskocil. Efficient semantic features for automated reasoning over large theories. In Q. Yang and M. Wooldridge, editors, Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 3084-3090. AAAI Press, 2015.
23. M. Kaufmann and J. S. Moore. An ACL2 tutorial. In Mohamed et al. [29], pages 17-21.
24. D. Kingma and J. Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
25. G. Klein, J. Andronick, K. Elphinstone, G. Heiser, D. Cock, P. Derrin, D. Elkaduwe, K. Engelhardt, R. Kolanski, M. Norrish, T. Sewell, H. Tuch, and S. Winwood. seL4: formal verification of an operating-system kernel. Commun. ACM, 53(6):107-115, 2010.
26. D. Kuehlwein and J. Urban. Learning from multiple proofs: First experiments. In P. Fontaine, R. A. Schmidt, and S. Schulz, editors, PAAR-2012, Volume 21 of EPiC Series, pages 82-94. EasyChair, 2013.
27. X. Leroy. Formal verification of a realistic compiler. Commun. ACM, 52(7):107-115, 2009.
28. T. Mikolov, M. Karafiát, L. Burget, J. Cernockỳ, and S. Khudanpur. Recurrent neural network based language model. In INTERSPEECH, Volume 2, page 3, 2010.
29. O. A. Mohamed, C. A. Muñoz, and S. Tahar, editors. Theorem Proving in Higher Order Logics, 21st International Conference, TPHOLs 2008, Montreal, Canada, August 18-21, 2008. Proceedings, Volume 5170 of LNCS. Springer, 2008.
30. B. T. Polyak and A. B. Juditsky. Acceleration of stochastic approximation by averaging. SIAM Journal on Control and Optimization, 30(4):838-855, 1992.
31. J. A. Robinson and A. Voronkov, editors. Handbook of Automated Reasoning (in 2 volumes). Elsevier and MIT Press, 2001.
32. S. Schulz. E - A Brainiac Theorem Prover. AI Commun., 15(2-3):111-126, 2002.
33. S. Sukhbaatar, J. Weston, R. Fergus, et al End-to-end memory networks. In Advances in Neural Information Processing Systems, pages 2431-2439, 2015.
34. J. Urban. MPTP 0.2: Design, implementation, and initial experiments. JAR, 37(1-2):21-43, 2006.
35. J. Urban and J. Vyskočil. Theorem proving in large formal mathematics as an emerging AI field. In M. P. Bonacina and M. E. Stickel, editors, Automated Reasoning and Mathematics: Essays in Memory of William McCune, Volume 7788 of LNAI, pages 240-257. Springer, 2013.
36. O. Vinyals and Q. Le. A neural conversational model. arXiv preprint arXiv:1506.05869, 2015.
37. M. Wenzel, L. C. Paulson, and T. Nipkow. The Isabelle framework. In Mohamed et al. [29], pages 33-38.
38. W. Zaremba and I. Sutskever. Learning to execute. arXiv preprint arXiv:1410.4615, 2014.