Advertisement

Checking Safety of Neural Networks with SMT Solvers: A Comparative Evaluation

  • Luca Pulina
  • Armando Tacchella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6934)

Abstract

In this paper we evaluate state-of-the-art SMT solvers on encodings of verification problems involving Multi-Layer Perceptrons (MLPs), a widely used type of neural network. Verification is a key technology to foster adoption of MLPs in safety-related applications, where stringent requirements about performance and robustness must be ensured and demonstrated. While safety problems for MLPs can be attacked solving Boolean combinations of linear arithmetic constraints, the generated encodings are hard for current state-of-the-art SMT solvers, limiting our ability to verify MLPs in practice.

Keywords

Empirical evaluation of SMT solvers Applications of Automated Reasoning Formal Methods for adaptive systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability, pp. 825–885. IOS Press, Amsterdam (2009)Google Scholar
  2. 2.
    Fontaine, P., Marion, J.Y., Merz, S., Nieto, L., Tiu, A.: Expressiveness+ automation+ soundness: Towards combining SMT solvers and interactive proof assistants. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 167–181. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    DeLine, R., Leino, K.R.M.: BoogiePL: A typed procedural language for checking object-oriented programs (2005)Google Scholar
  4. 4.
    Ray, S.: Connecting External Deduction Tools with ACL2. In: Scalable Techniques for Formal Verification, pp. 195–216 (2010)Google Scholar
  5. 5.
    Armando, A., Mantovani, J., Platania, L.: Bounded model checking of software using SMT solvers instead of SAT solvers. International Journal on Software Tools for Technology Transfer (STTT) 11(1), 69–83 (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Hoang, T.A., Binh, N.N.: Extending CREST with Multiple SMT Solvers and Real Arithmetic. In: 2010 Second International Conference on Knowledge and Systems Engineering (KSE), pp. 183–187. IEEE, Los Alamitos (2010)Google Scholar
  7. 7.
    Barrett, C., de Moura, L., Stump, A.: SMT-COMP: Satisfiability Modulo Theories Competition. In: Etessami, K., Rajamani, S. (eds.) CAV 2005. LNCS, vol. 3576, pp. 20–23. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Bishop, C.M.: Neural networks and their applications. Review of Scientific Instruments 65(6), 1803–1832 (2009)CrossRefGoogle Scholar
  9. 9.
    Schumann, J., Liu, Y. (eds.): Applications of Neural Networks in High Assurance Systems. SCI, vol. 268. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  10. 10.
    Haykin, S.: Neural networks: a comprehensive foundation. Prentice Hall, Englewood Cliffs (2008)zbMATHGoogle Scholar
  11. 11.
    Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989)CrossRefGoogle Scholar
  12. 12.
    Cok, D.R.: The SMT-LIBv2 Language and Tools: A Tutorial (2011), http://www.grammatech.com/resources/smt/
  13. 13.
    Franzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient solving of large non-linear arithmetic constraint systems with complex boolean structure. Journal on Satisfiability, Boolean Modeling and Computation 1, 209–236 (2007)zbMATHGoogle Scholar
  14. 14.
    Bruttomesso, R., Cimatti, A., Franzén, A., Griggio, A., Sebastiani, R.: The MathSAT 4 SMT Solver. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 299–303. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Dutertre, B., De Moura, L.: A fast linear-arithmetic solver for DPLL (T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Fumagalli, M., Gijsberts, A., Ivaldi, S., Jamone, L., Metta, G., Natale, L., Nori, F., Sandini, G.: Learning to Exploit Proximal Force Sensing: a Comparison Approach. In: Sigaud, O., Peters, J. (eds.) From Motor Learning to Interaction Learning in Robots. SCI, vol. 264, pp. 149–167. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Luca Pulina
    • 1
  • Armando Tacchella
    • 2
  1. 1.DEISUniversity of SassariSassariItaly
  2. 2.DISTUniversity of GenovaGenovaItaly

Personalised recommendations