Skip to main content

Formal Specification for Deep Neural Networks

  • Conference paper
  • First Online:
Automated Technology for Verification and Analysis (ATVA 2018)

Abstract

The increasing use of deep neural networks in a variety of applications, including some safety-critical ones, has brought renewed interest in the topic of verification of neural networks. However, verification is most meaningful when performed with high-quality formal specifications. In this paper, we survey the landscape of formal specification for deep neural networks, and discuss the opportunities and challenges for formal methods for this domain.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    An early version of this paper appeared in [51].

References

  1. Albarghouthi, A., D’Antoni, L., Drews, S., Nori, A.: Fairness as a program property (2016), arXiv:1610.06067

  2. Albarghouthi, A., D’Antoni, L., Drews, S., Nori, A.V.: Fairsquare: probabilistic verification of program fairness. In: Proceedings of the ACM on Programming Languages (2017)

    Article  Google Scholar 

  3. Alipanahi, B., Delong, A., Weirauch, M.T., Frey, B.J.: Predicting the sequence specificities of DNA-and RNA-binding proteins by deep learning. Nat. Biotechnol. 33, 831–838 (2015)

    Article  Google Scholar 

  4. Amodei, D., Olah, C., Steinhardt, J., Christiano, P.F., Schulman, J., Mané, D.: Concrete problems in AI safety. ArXiV e-prints abs/1606.06565 (2016)

  5. Bastani, O., Ioannou, Y., Lampropoulos, L., Vytiniotis, D., Nori, A., Criminisi, A.: Measuring neural net robustness with constraints. In: Lee, D.D., Sugiyama, M., Luxburg, U.V., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems (NIPS), vol. 29, pp. 2613–2621. MIT Press, Cambridge (2016)

    Google Scholar 

  6. Binns, R.: Fairness in machine learning: lessons from political philosophy (2017), arXiv:1712.03586

  7. Bojarski, M., et al.: End to end learning for self-driving cars. arXiv preprint arXiv:1604.07316 (2016)

  8. Cai, J., Shin, R., Song, D.: Making neural programming architectures generalize via recursion. arXiv preprint arXiv:1704.06611 (2017)

  9. Carlini, N., Wagner, D.: Towards evaluating the robustness of neural networks. In: IEEE Symposium on Security and Privacy (SP) (2017)

    Google Scholar 

  10. Carpenter, B., et al.: Stan: a probabilistic programming language. J. Stat. Softw. 76(1), 1–32 (2017)

    Article  Google Scholar 

  11. Cheng, C.-H., Nührenberg, G., Ruess, H.: Maximum resilience of artificial neural networks. In: D’Souza, D., Narayan Kumar, K. (eds.) ATVA 2017. LNCS, vol. 10482, pp. 251–268. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68167-2_18

    Chapter  Google Scholar 

  12. Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)

    Article  Google Scholar 

  13. Dahl, G.E., Stokes, J.W., Deng, L., Yu, D.: Large-scale malware classification using random projections and neural networks. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 3422–3426. IEEE (2013)

    Google Scholar 

  14. Dai, J., et al.: Deformable convolutional networks. In: IEEE International Conference on Computer Vision (2017)

    Google Scholar 

  15. Dreossi, T., Donzé, A., Seshia, S.A.: Compositional falsification of cyber-physical systems with machine learning components. In: NASA Formal Methods Symposium (2017)

    Google Scholar 

  16. Dreossi, T., Donzé, A., Seshia, S.A.: Compositional falsification of cyber-physical systems with machine learning components. In: Barrett, C., Davies, M., Kahsai, T. (eds.) NFM 2017. LNCS, vol. 10227, pp. 357–372. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57288-8_26

    Chapter  Google Scholar 

  17. Dreossi, T., Ghosh, S., Yue, X., Keutzer, K., Sangiovanni-Vincentelli, A., Seshia, S.A.: Counterexample-guided data augmentation. In: 27th International Joint Conference on Artificial Intelligence (IJCAI) (2018)

    Google Scholar 

  18. Dreossi, T., Jha, S., Seshia, S.A.: Semantic adversarial deep learning. In: 30th International Conference on Computer Aided Verification (CAV) (2018)

    Chapter  Google Scholar 

  19. Dutta, S., Jha, S., Sanakaranarayanan, S., Tiwari, A.: Output range analysis for deep neural networks (2017), arXiv:1709.09130

  20. Dvijotham, K., Stanforth, R., Gowal, S., Mann, T., Kohli, P.: A dual approach to scalable verification of deep networks (2018), arXiv:1803.06567

  21. Fawzi, A., Frossard, P.: Manitest: Are classifiers really invariant? (2017), arXiv:1507.06535

  22. Fremont, D., Yue, X., Dreossi, T., Ghosh, S., Sangiovanni-Vincentelli, A.L., Seshia, S.A.: Scenic: Language-based scene generation. Technical report UCB/EECS-2018-8. EECS Department, University of California, Berkeley, April 2018. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-8.html

  23. Friedler, S.A., Scheidegger, C., Venkatasubramanian, S.: On the (im) possibility of fairness (2016), arXiv:1609.07236

  24. Friedler, S.A., Scheidegger, C., Venkatasubramanian, S., Choudhary, S., Hamilton, E.P., Roth, D.: A comparative study of fairness-enhancing interventions in machine learning (2018), arXiv:1802.04422

  25. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016). http://goodfeli.github.io/dlbook/

  26. Goodfellow, I., Lee, H., Le, Q.V., Saxe, A., Ng, A.Y.: Measuring invariances in deep networks. In: Advances in Neural Information Processing Systems (2009)

    Google Scholar 

  27. Goodfellow, I.J., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples (2014), arXiv:1412.6572

  28. Goodman, N.D., Mansinghka, V.K., Roy, D., Bonawitz, K., Tenenbaum, J.B.: Church: a language for generative models. In: Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence, pp. 220–229. UAI’08 (2008)

    Google Scholar 

  29. Gordon, A.D., Henzinger, T.A., Nori, A.V., Rajamani, S.K.: Probabilistic programming. In: FOSE 2014, pp. 167–181. ACM (2014)

    Google Scholar 

  30. Graves, A., Wayne, G., Danihelka, I.: Neural turing machines. arXiv preprint arXiv:1410.5401 (2014)

  31. Hardt, M., Price, E., Srebro, N., et al.: Equality of opportunity in supervised learning. In: Advances in Neural Information Processing Systems (2016)

    Google Scholar 

  32. Huang, X., Kwiatkowska, M., Wang, S., Wu, M.: Safety verification of deep neural networks. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 3–29. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_1

    Chapter  Google Scholar 

  33. Kaelbling, L.P., Littman, M.L., Moore, A.W.: Reinforcement learning: a survey. J. Artif. Intell. Res. 4, 237–285 (1996)

    Article  Google Scholar 

  34. Kanbak, C., Moosavi-Dezfooli, S.M., Frossard, P.: Geometric robustness of deep networks: analysis and improvement (2017), arXiv:1711.09115

  35. Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097–1105 (2012)

    Google Scholar 

  36. Kusner, M.J., Loftus, J., Russell, C., Silva, R.: Counterfactual fairness. In: Advances in Neural Information Processing Systems (2017)

    Google Scholar 

  37. Lowe, D.G.: Object recognition from local scale-invariant features. In: IEEE International Conference on Computer Vision (1999)

    Google Scholar 

  38. Madry, A., Makelov, A., Schmidt, L., Tsipras, D., Vladu, A.: Towards deep learning models resistant to adversarial attacks (2017), arXiv:1706.06083

  39. Milch, B., Marthi, B., Russell, S.: Blog: Relational modeling with unknown objects. In: ICML 2004 Workshop on Statistical Relational Learning and its Connections to Other Fields, pp. 67–73 (2004)

    Google Scholar 

  40. Mnih, V., et al.: Human-level control through deep reinforcement learning. Nature 518(7540), 529 (2015)

    Article  Google Scholar 

  41. NVIDIA: Nvidia tegra drive px: Self-driving car computer (2015), http://www.nvidia.com/object/drive-px.html

  42. Papernot, N., McDaniel, P., Jha, S., Fredrikson, M., Celik, Z.B., Swami, A.: The limitations of deep learning in adversarial settings. In: Proceedings of the 1st IEEE European Symposium on Security and Privacy. arXiv preprint arXiv:1511.07528 (2016)

  43. Papernot, N., McDaniel, P., Wu, X., Jha, S., Swami, A.: Distillation as a defense to adversarial perturbations against deep neural networks. arXiv preprint arXiv:1511.04508 (2015)

  44. Pei, K., Cao, Y., Yang, J., Jana, S.: Deepxplore: automated whitebox testing of deep learning systems. In: Proceedings of the 26th Symposium on Operating Systems Principles, pp. 1–18. ACM (2017)

    Google Scholar 

  45. Pfeffer, A.: Figaro: an object-oriented probabilistic programming language. Technical report, Charles River Analytics (2009)

    Google Scholar 

  46. Rodrigues, P., Costa, J.F., Siegelmann, H.T.: Verifying properties of neural networks. In: Mira, J., Prieto, A. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 158–165. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45720-8_19

    Chapter  Google Scholar 

  47. Russell, S., et al.: Letter to the editor: research priorities for robust and beneficial artif icial intelligence: an open letter. AI Mag. 36(4), 3–4 (2015)

    Article  Google Scholar 

  48. Sadigh, D., Kim, E.S., Coogan, S., Sastry, S., Seshia, S.A.: A learning based approach to control synthesis of markov decision processes for linear temporal logic specifications. In: Proceedings of the 53rd IEEE Conference on Decision and Control (CDC), pp. 1091–1096, December 2014

    Google Scholar 

  49. Selsam, D., Liang, P., Dill, D.L.: Developing bug-free machine learning systems with formal mathematics. In: International Conference on Machine Learning, pp. 3047–3056 (2017)

    Google Scholar 

  50. Seshia, S.A.: Compositional verification without compositional specification for learning-based systems. Technical report UCB/EECS-2017-164. EECS Department, University of California, Berkeley, November 2017. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2017/EECS-2017-164.html

  51. Seshia, S.A., et al.: Formal specification for deep neural networks. Technical report UCB/EECS-2018-25. EECS Department, University of California, Berkeley, May 2018. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-25.html

  52. Seshia, S.A., Sadigh, D., Sastry, S.S.: Towards Verified Artificial Intelligence. ArXiv e-prints, July 2016

    Google Scholar 

  53. Shin, E.C.R., Song, D., Moazzezi, R.: Recognizing functions in binaries with neural networks. In: 24th USENIX Security Symposium (USENIX Security 15), pp. 611–626 (2015)

    Google Scholar 

  54. Szegedy, C., et al.: Intriguing properties of neural networks (2013), arXiv:1312.6199

  55. Taylor, B.J., Darrah, M.A.: Rule extraction as a formal method for the verification and validation of neural networks. In: IEEE International Joint Conference on Neural Networks (IJCNN), vol. 5, pp. 2915–2920. IEEE (2005)

    Google Scholar 

  56. Terauchi, T., Aiken, A.: Secure information flow as a safety problem. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 352–367. Springer, Heidelberg (2005). https://doi.org/10.1007/11547662_24

    Chapter  Google Scholar 

  57. Wen, M., Ehlers, R., Topcu, U.: Correct-by-synthesis reinforcement learning with temporal logic constraints. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4983–4990 (2015)

    Google Scholar 

  58. Weng, T.W., et al.: Evaluating the robustness of neural networks: an extreme value theory approach (2018), arXiv:1801.10578

  59. You, S., Ding, D., Canini, K., Pfeifer, J., Gupta, M.: Deep lattice networks and partial monotonic functions. In: Advances in Neural Information Processing Systems (2017)

    Google Scholar 

Download references

Acknowledgments

The work of the authors on this paper was funded in part by the NSF VeHICaL project (#1545126), NSF projects #1646208 and #1739816, NSF Graduate Research Fellowships, DARPA under agreement number FA8750-16-C0043, the DARPA Assured Autonomy program, Berkeley Deep Drive, and by Toyota under the iCyPhy center. This paper was the outcome of discussions amongst the co-authors in early 2018. It has additionally benefited from conversations with Somesh Jha, Susmit Jha, Pushmeet Kohli, Aditya Nori, Jerry Zhu, and several participants in Dagstuhl Seminar 18121.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sanjit A. Seshia .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Seshia, S.A. et al. (2018). Formal Specification for Deep Neural Networks. In: Lahiri, S., Wang, C. (eds) Automated Technology for Verification and Analysis. ATVA 2018. Lecture Notes in Computer Science(), vol 11138. Springer, Cham. https://doi.org/10.1007/978-3-030-01090-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-01090-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01089-8

  • Online ISBN: 978-3-030-01090-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics