Skip to main content

Simplifying Neural Networks Using Formal Verification

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12229))

Included in the following conference series:

Abstract

Deep neural network (DNN) verification is an emerging field, with diverse verification engines quickly becoming available. Demonstrating the effectiveness of these engines on real-world DNNs is an important step towards their wider adoption. We present a tool that can leverage existing verification engines in performing a novel application: neural network simplification, through the reduction of the size of a DNN without harming its accuracy. We report on the work-flow of the simplification process, and demonstrate its potential significance and applicability on a family of real-world DNNs for aircraft collision avoidance, whose sizes we were able to reduce by as much as 10%.

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 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
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

Similar content being viewed by others

References

  1. Bastani, O., Ioannou, Y., Lampropoulos, L., Vytiniotis, D., Nori, A., Criminisi, A.: Measuring neural net robustness with constraints. In: Proceedings of 30th Conference on Neural Information Processing Systems (NIPS) (2016)

    Google Scholar 

  2. Bojarski, M., et al.: End to end learning for self-driving cars. Technical report (2016). http://arxiv.org/abs/1604.07316

  3. Bunel, R., Turkaslan, I., Torr, P.H., Kohli, P., Kumar, M.P.: Piecewise linear neural network verification: a comparative study. Technical report (2017). https://arxiv.org/abs/1711.00455v1

  4. Carlini, N., Katz, G., Barrett, C., Dill, D.: Provably minimally-distorted adversarial examples. Technical report (2017). https://arxiv.org/abs/1709.10207

  5. Collobert, R., Weston, J., Bottou, L., Karlen, M., Kavukcuoglu, K., Kuksa, P.: Natural language processing (almost) from scratch. J. Mach. Learn. Res. (JMLR) 12, 2493–2537 (2011)

    MATH  Google Scholar 

  6. Dutta, S., Jha, S., Sanakaranarayanan, S., Tiwari, A.: Output range analysis for deep neural networks. In: Proceedings of 10th NASA Formal Methods Symposium (NFM), pp. 121–138 (2018)

    Google Scholar 

  7. Ehlers, R.: Formal verification of piece-wise linear feed-forward neural networks. In: Proceedings of 15th International Symposium on Automated Technology for Verification and Analysis (ATVA), pp. 269–286 (2017)

    Google Scholar 

  8. Elboher, Y., Gottschlich, J., Katz, G.: An abstraction-based framework for neural network verification. Technical report (2019). http://arxiv.org/abs/1910.14574

  9. Gehr, T., Mirman, M., Drachsler-Cohen, D., Tsankov, P., Chaudhuri, S., Vechev, M.: AI2: safety and robustness certification of neural networks with abstract interpretation. In: Proceedings of 39th IEEE Symposium on Security and Privacy (S&P) (2018)

    Google Scholar 

  10. Gokulanathan, S., Feldsher, A., Malca, A., Barrett, C., Katz, G.: The NNSimplify Code (2020). https://drive.google.com/open?id=19TbPS7P9fo-2tRXo8ENnggLY1LxxPCd1

  11. Gopinath, D., Katz, G., Pǎsǎreanu, C., Barrett, C.: DeepSafe: a data-driven approach for checking adversarial robustness in neural networks. In: Proceedings of 16th International Symposium on Automated Technology for Verification and Analysis (ATVA), pp. 3–19 (2018)

    Google Scholar 

  12. Han, S., Mao, H., Dally, W.: Deep compression: compressing deep neural networks with pruning, trained quantization and Huffman coding. Technical report (2015). http://arxiv.org/abs/1510.00149

  13. Howard, A., et al.: MobileNets: efficient convolutional neural networks for mobile vision applications. Technical report (2017). http://arxiv.org/abs/1704.04861

  14. 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 

  15. Iandola, F.N., Han, S., Moskewicz, M.W., Ashraf, K., Dally, W.J., Keutzer, K.: SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and \(<\)0.5 MB model size. Technical report (2016). http://arxiv.org/abs/1602.07360

  16. Julian, K.: NNet Format (2018). https://github.com/sisl/NNet

  17. Julian, K., Kochenderfer, M., Owen, M.: Deep neural network compression for aircraft collision avoidance systems. J. Guid. Control Dyn. 42(3), 598–608 (2019)

    Article  Google Scholar 

  18. Julian, K.D., Lopez, J., Brush, J.S., Owen, M.P., Kochenderfer, M.J.: Policy compression for aircraft collision avoidance systems. In: Proceedings of 35th Digital Avionics Systems Conference (DASC), pp. 1–10 (2016)

    Google Scholar 

  19. Katz, G., Barrett, C., Dill, D., Julian, K., Kochenderfer, M.: Reluplex: an efficient SMT solver for verifying deep neural networks. In Proceedings of 29th International Conference on Computer Aided Verification (CAV), pp. 97–117 (2017)

    Google Scholar 

  20. Katz, G., Barrett, C., Dill, D., Julian, K., Kochenderfer, M.: Towards proving the adversarial robustness of deep neural networks. In: Proceedings of 1st Workshop on Formal Verification of Autonomous Vehicles (FVAV), pp. 19–26 (2017)

    Google Scholar 

  21. Katz, G., et al.: The Marabou framework for verification and analysis of deep neural networks. In: Proceedings of 31st International Conference on Computer Aided Verification (CAV), pp. 443–452 (2019)

    Google Scholar 

  22. Kazak, Y., Barrett, C., Katz, G., Schapira, M.: Verifying deep-RL-driven systems. In: Proceedings of 1st ACM SIGCOMM Workshop on Network Meets AI & ML (NetAI), pp. 83–89 (2019)

    Google Scholar 

  23. Kuper, L., Katz, G., Gottschlich, J., Julian, K., Barrett, C., Kochenderfer, M.: Toward scalable verification for safety-critical deep networks. Technical report (2018). https://arxiv.org/abs/1801.05950

  24. Liu, C., Arnon, T., Lazarus, C., Barrett, C., Kochenderfer, M.: Algorithms for verifying deep neural networks. Technical report (2019). http://arxiv.org/abs/1903.06758

  25. Lomuscio, A., Maganti, L.: An approach to reachability analysis for feed-forward ReLU neural networks. Technical report (2017). http://arxiv.org/abs/1706.07351

  26. Narodytska, N., Kasiviswanathan, S., Ryzhyk, L., Sagiv, M., Walsh, T.: Verifying properties of binarized deep neural networks. Technical report (2017). http://arxiv.org/abs/1709.06662

  27. Silver, D., et al.: Mastering the game of Go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016)

    Article  Google Scholar 

  28. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. Technical report (2014). http://arxiv.org/abs/1409.1556

  29. Sun, X., Khedr, H., Shoukry, Y.: Formal verification of neural network controlled autonomous systems. In: Proceedings of 22nd ACM International Conference on Hybrid Systems: Computation and Control (HSCC), pp. 147–156 (2019)

    Google Scholar 

  30. Szegedy, C., et al.: Intriguing properties of neural networks. Technical report (2013). http://arxiv.org/abs/1312.6199

  31. Tjeng, V., Xiao, K., Tedrake, R.: Evaluating robustness of neural networks with mixed integer programming. In: Proceedings of 7th International Conference on Learning Representations (ICLR) (2019)

    Google Scholar 

  32. Wang, S., Pei, K., Whitehouse, J., Yang, J., Jana, S.: Formal security analysis of neural networks using symbolic intervals. Technical report (2018). http://arxiv.org/abs/1804.10829

Download references

Acknowledgements

This project was partially supported by grants from the Binational Science Foundation (2017662), the Israel Science Foundation (683/18), and the National Science Foundation (1814369).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guy Katz .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gokulanathan, S., Feldsher, A., Malca, A., Barrett, C., Katz, G. (2020). Simplifying Neural Networks Using Formal Verification. In: Lee, R., Jha, S., Mavridou, A., Giannakopoulou, D. (eds) NASA Formal Methods. NFM 2020. Lecture Notes in Computer Science(), vol 12229. Springer, Cham. https://doi.org/10.1007/978-3-030-55754-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-55754-6_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-55753-9

  • Online ISBN: 978-3-030-55754-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics