Abstract
Machine learning is becoming increasingly important to control the behavior of safety and financially critical components in sophisticated environments, where the inability to understand learned components in general, and neural nets in particular, poses serious obstacles to their adoption. Explainability and interpretability methods for learned systems have gained considerable academic attention, but the focus of current approaches on only one aspect of explanation, at a fixed level of abstraction, and limited if any formal guarantees, prevents those explanations from being digestible by the relevant stakeholders (e.g., end users, certification authorities, engineers) with their diverse backgrounds and situation-specific needs. We introduce Fanoos, a framework for combining formal verification techniques, heuristic search, and user interaction to explore explanations at the desired level of granularity and fidelity. We demonstrate the ability of Fanoos to produce and adjust the abstractness of explanations in response to user requests on a learned controller for an inverted double pendulum and on a learned CPU usage model.
This material is based upon work supported by the United States Air Force and DARPA under Contract No. FA8750-18-C-0092. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force and DARPA.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
In the case of interval arithmetic, this over-approximation and inclusion of additional elements is often called the “wrapping effect” [42].
- 3.
Elements of our abstract state refinement algorithm may be analogous to CEGAR and its standard extensions—for instance, we perform sampling-based feasibility checks prior to SAT-checks, which may be comparable to spuriousness checks in CEGAR. However, to avoid implying a stringent adherence to canon (i.e., [16] verbatim), we use a different name.
- 4.
Strictly speaking, we could discuss a box containing \(S_I\) (i.e., a superset), but introducing an auxiliary, potentially larger definition domain might add confusion while giving little benefit.
- 5.
Setting thresholds low enough to ensure each transaction is described would result in a deluge of highly redundant, low-precision rules lacking most practical value, a phenomena know as the “rare itemset problem” [50].
- 6.
Dataset at https://www.openml.org/api/v1/json/data/562.
References
Adadi, A., Berrada, M.: Peeking inside the black-box: a survey on explainable artificial intelligence (XAI). IEEE Access 6, 52138–52160 (2018)
Adam, S.P., Karras, D.A., Magoulas, G.D., Vrahatis, M.N.: Reliable estimation of a neural network’s domain of validity through interval analysis based inversion. In: 2015 International Joint Conference on Neural Networks, IJCNN 2015, Killarney, Ireland, 12–17 July 2015, pp. 1–8 (2015). https://doi.org/10.1109/IJCNN.2015.7280794
Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data, Washington, DC, USA, 26–28 May 1993, vol. 22, pp. 207–216. ACM (1993)
Andrews, R., Diederich, J., Tickle, A.: Survey and critique of techniques for extracting rules from trained artificial neural networks. Knowl.-Based Syst. 6, 373–389 (1995). https://doi.org/10.1016/0950-7051(96)81920-4
Anjomshoae, S., Najjar, A., Calvaresi, D., Främling, K.: Explainable agents and robots: results from a systematic literature review. In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, pp. 1078–1088. International Foundation for Autonomous Agents and Multiagent Systems (2019)
Arya, V., et al.: One explanation does not fit all: a toolkit and taxonomy of AI explainability techniques. CoRR abs/1909.03012 (2019)
Bayani, D.: Code for Fanoos: multi-resolution, multi-strength, interactive explanations for learned systems (2021). https://doi.org/10.5281/zenodo.5513079. Method of distribution is Zenodo, distributed in October, 2021
Bayani, D., Mitsch, S.: Fanoos: multi-resolution, multi-strength, interactive explanations for learned systems. CoRR abs/2006.12453 (2020)
Benz, A., Jäger, G., Van Rooij, R.: Game Theory and Pragmatics. Springer, Heidelberg (2005). https://doi.org/10.1057/9780230285897
Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y., et al.: Bounded model checking. Adv. Comput. 58(11), 117–148 (2003)
Biran, O., Cotton, C.: Explanation and justification in machine learning: a survey. In: IJCAI-17 Workshop on Explainable AI (XAI), vol. 8, p. 1 (2017)
Bunel, R., Turkaslan, I., Torr, P.H.S., Kohli, P., Mudigonda, P.K.: A unified view of piecewise linear neural network verification. In: Bengio, S., Wallach, H.M., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, 3–8 December 2018, Montréal, Canada, pp. 4795–4804 (2018)
Chakraborti, T., Kulkarni, A., Sreedharan, S., Smith, D.E., Kambhampati, S.: Explicability? Legibility? Predictability? Transparency? Privacy? Security? The emerging landscape of interpretable agent behavior. In: Proceedings of the International Conference on Automated Planning and Scheduling, vol. 29, pp. 86–96 (2019)
Chuang, J., Ramage, D., Manning, C., Heer, J.: Interpretation and trust: designing model-driven visualizations for text analysis. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 443–452. ACM (2012)
Clarke, E., Fehnker, A., Han, Z., Krogh, B., Stursberg, O., Theobald, M.: Verification of hybrid systems based on counterexample-guided abstraction refinement. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 192–207. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36577-X_14
Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_15
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the 4th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pp. 238–252 (1977)
David, Q.: Design issues in adaptive control. IEEE Trans. Autom. Control 33(1), 50–58 (1988)
de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24
Driescher, A., Korn, U.: Checking stability of neural NARX models: an interval approach. IFAC Proc. Vol. 30(6), 1005–1010 (1997)
Dvijotham, K., Stanforth, R., Gowal, S., Mann, T.A., Kohli, P.: A dual approach to scalable verification of deep networks. In: Globerson, A., Silva, R. (eds.) Proceedings of the Thirty-Fourth Conference on Uncertainty in Artificial Intelligence, UAI 2018, Monterey, California, USA, 6–10 August 2018, pp. 550–559. AUAI Press (2018)
Ehlers, R.: Formal verification of piece-wise linear feed-forward neural networks. In: D’Souza, D., Narayan Kumar, K. (eds.) ATVA 2017. LNCS, vol. 10482, pp. 269–286. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68167-2_19
Etchells, T.A., Lisboa, P.J.: Orthogonal search-based rule extraction (OSRE) for trained neural networks: a practical and efficient approach. IEEE Trans. Neural Netw. 17(2), 374–384 (2006)
Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing directive 95/46/EC (General Data Protection Regulation) (2016)
Fern, A.: Don’t get fooled by explanations. Invited Talk, IJCAI-XAI (2020). Recording at: https://ijcai20.org/w41/. Schedule at: https://sites.google.com/view/xai2020/home
Floridi, L.: The method of levels of abstraction. Mind. Mach. 18(3), 303–329 (2008)
Friedrich, G., Zanker, M.: A taxonomy for generating explanations in recommender systems. AI Mag. 32(3), 90–98 (2011)
Garcıa, J., Fernández, F.: A comprehensive survey on safe reinforcement learning. J. Mach. Learn. Res. 16(1), 1437–1480 (2015)
Gehr, T., Mirman, M., Drachsler-Cohen, D., Tsankov, P., Chaudhuri, S., Vechev, M.T.: AI2: safety and robustness certification of neural networks with abstract interpretation. In: 2018 IEEE Symposium on Security and Privacy, SP 2018, Proceedings, 21–23 May 2018, San Francisco, California, USA, pp. 3–18. IEEE Computer Society (2018). https://doi.org/10.1109/SP.2018.00058
Guidotti, R., Monreale, A., Ruggieri, S., Turini, F., Giannotti, F., Pedreschi, D.: A survey of methods for explaining black box models. ACM Comput. Surv. (CSUR) 51(5), 93 (2019)
Gunning, D., Aha, D.: DARPA’s explainable artificial intelligence (XAI) program. AI Mag. 40(2), 44–58 (2019). https://doi.org/10.1609/aimag.v40i2.2850
Hailesilassie, T.: Rule extraction algorithm for deep neural networks: a review. arXiv preprint arXiv:1610.05267 (2016)
Han, J., Fu, Y.: Discovery of multiple-level association rules from large databases. In: VLDB, vol. 95, pp. 420–431. Citeseer (1995)
Han, J., Fu, Y.: Mining multiple-level association rules in large databases. IEEE Trans. Knowl. Data Eng. 11(5), 798–805 (1999)
Hayes, B., Scassellati, B.: Autonomously constructing hierarchical task networks for planning and human-robot collaboration. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 5469–5476. IEEE (2016)
Hayes, B., Shah, J.A.: Improving robot controller transparency through autonomous policy explanation. In: 2017 12th ACM/IEEE International Conference on Human-Robot Interaction (HRI), pp. 303–312. IEEE (2017)
Hipp, J., Güntzer, U., Nakhaeizadeh, G.: Algorithms for association rule mining- a general survey and comparison. SIGKDD Explor. 2(1), 58–64 (2000)
Hostetler, J., Fern, A., Dietterich, T.G.: Progressive abstraction refinement for sparse sampling. In: Meila, M., Heskes, T. (eds.) Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, UAI 2015, 12–16 July 2015, Amsterdam, The Netherlands, pp. 365–374. AUAI Press (2015)
Huang, S.H., Held, D., Abbeel, P., Dragan, A.D.: Enabling robots to communicate their objectives. Auton. Robot. 43(2), 309–326 (2019). https://doi.org/10.1007/s10514-018-9771-0
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
Katz, G., Barrett, C., Dill, D.L., Julian, K., Kochenderfer, M.J.: Reluplex: an efficient SMT solver for verifying deep neural networks. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017, Part I. LNCS, vol. 10426, pp. 97–117. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_5
Kearfott, R.B.: Interval computations: introduction, uses, and resources. Euromath Bull. 2(1), 95–112 (1996)
Kellert, S.H.: In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press (1993)
Kim, J., Rohrbach, A., Darrell, T., Canny, J.F., Akata, Z.: Textual explanations for self-driving vehicles (2018). https://doi.org/10.1007/978-3-030-01216-8_35
Koul, A., Fern, A., Greydanus, S.: Learning finite state representations of recurrent policy networks. In: 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, 6–9 May 2019. OpenReview.net (2019)
Levien, R., Tan, S.: Double pendulum: an experiment in chaos. Am. J. Phys. 61(11), 1038–1044 (1993)
Lipton, Z.C.: The mythos of model interpretability. arXiv preprint arXiv:1606.03490 (2016)
Liskov, B.: Keynote address-data abstraction and hierarchy. In: Addendum to the Proceedings on Object-Oriented Programming Systems, Languages and Applications (Addendum), pp. 17–34 (1987)
Liskov, B.H., Wing, J.M.: A behavioral notion of subtyping. ACM Trans. Program. Lang. Syst. (TOPLAS) 16(6), 1811–1841 (1994)
Liu, B., Hsu, W., Ma, Y.: Mining association rules with multiple minimum supports. In: Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 337–341 (1999)
Miller, T.: Explanation in artificial intelligence: insights from the social sciences. Artif. Intell. 267, 1–38 (2018)
Miller, T., Howe, P., Sonenberg, L.: Explainable AI: beware of inmates running the asylum or: how I learnt to stop worrying and love the social and behavioural sciences. arXiv preprint arXiv:1712.00547 (2017)
Mirman, M., Gehr, T., Vechev, M.: Differentiable abstract interpretation for provably robust neural networks. In: International Conference on Machine Learning, pp. 3575–3583 (2018)
Mohseni-Kabir, A., Rich, C., Chernova, S., Sidner, C.L., Miller, D.: Interactive hierarchical task learning from a single demonstration. In: Proceedings of the Tenth Annual ACM/IEEE International Conference on Human-Robot Interaction, pp. 205–212. ACM (2015)
Moore, R.E.: Interval Analysis, vol. 4. Prentice-Hall, Englewood Cliffs (1966)
Muggleton, S.: Inductive logic programming: issues, results and the challenge of learning language in logic. Artif. Intell. 114(1–2), 283–296 (1999)
Murdoch, W.J., Szlam, A.: Automatic rule extraction from long short term memory networks. arXiv preprint arXiv:1702.02540 (2017)
Neema, S.: Assured autonomy (2017). https://www.darpa.mil/attachments/AssuredAutonomyProposersDay_Program%20Brief.pdf
Papadimitriou, A., Symeonidis, P., Manolopoulos, Y.: A generalized taxonomy of explanations styles for traditional and social recommender systems. Data Min. Knowl. Disc. 24(3), 555–583 (2012)
Perera, V., Selvaraj, S.P., Rosenthal, S., Veloso, M.M.: Dynamic generation and refinement of robot verbalization. In: 25th IEEE International Symposium on Robot and Human Interactive Communication, RO-MAN 2016, New York, NY, USA, 26–31 August 2016, pp. 212–218. IEEE (2016). https://doi.org/10.1109/ROMAN.2016.7745133
Pulina, L., Tacchella, A.: An abstraction-refinement approach to verification of artificial neural networks. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 243–257. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14295-6_24
Raffin, A.: RL baselines zoo (2018). https://web.archive.org/web/20190524144858/https://github.com/araffin/rl-baselines-zoo
Ribeiro, M.T., Singh, S., Guestrin, C.: “Why should I trust you?”: explaining the predictions of any classifier. In: Krishnapuram, B., Shah, M., Smola, A.J., Aggarwal, C.C., Shen, D., Rastogi, R. (eds.) Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016, pp. 1135–1144. ACM (2016). https://doi.org/10.1145/2939672.2939778
Richardson, A., Rosenfeld, A.: A survey of interpretability and explainability in human-agent systems. In: XAI Workshop on Explainable Artificial Intelligence, pp. 137–143 (2018)
Roberts, M., et al.: What was I planning to do. In: ICAPS Workshop on Explainable Planning, pp. 58–66 (2018)
Rosenthal, S., Biswas, J., Veloso, M.: An effective personal mobile robot agent through symbiotic human-robot interaction. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 915–922. International Foundation for Autonomous Agents and Multiagent Systems (2010)
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347 (2017)
Setiono, R., Liu, H.: Understanding neural networks via rule extraction. In: IJCAI, vol. 1, pp. 480–485 (1995)
Singh, G., Ganvir, R., Püschel, M., Vechev, M.T.: Beyond the single neuron convex barrier for neural network certification. In: Wallach, H.M., Larochelle, H., Beygelzimer, A., d’Alché-Buc, F., Fox, E.B., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, 8–14 December 2019, Vancouver, BC, Canada, pp. 15072–15083 (2019)
Sreedharan, S., Madhusoodanan, M.P., Srivastava, S., Kambhampati, S.: Plan explanation through search in an abstract model space. In: International Conference on Automated Planning and Scheduling (ICAPS) Workshop on Explainable Planning, pp. 67–75 (2018)
Srikant, R., Agrawal, R.: Mining generalized association rules. In: Dayal, U., Gray, P.M.D., Nishio, S. (eds.) VLDB 1995, Proceedings of 21st International Conference on Very Large Data Bases, 11–15 September 1995, Zurich, Switzerland, pp. 407–419. Morgan Kaufmann (1995)
International Standardization: ISO/IEC 7498–1: 1994 information technology-open systems interconnection-basic reference model: the basic model. International Standard ISOIEC 74981, 59 (1996)
Taylor, B.J., Darrah, M.A.: Rule extraction as a formal method for the verification and validation of neural networks. In: 2005 Proceedings of 2005 IEEE International Joint Conference on Neural Networks, vol. 5, pp. 2915–2920. IEEE (2005)
Tennent, R.D.: The denotational semantics of programming languages. Commun. ACM 19(8), 437–453 (1976). https://doi.org/10.1145/360303.360308
Thrun, S.: Extracting rules from artificial neural networks with distributed representations. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) 1994 Advances in Neural Information Processing Systems 7, NIPS Conference, Denver, Colorado, USA, pp. 505–512. MIT Press (1994)
Tjeng, V., Xiao, K., Tedrake, R.: Verifying neural networks with mixed integer programming. CoRR abs/1711.07356 (2017). http://arxiv.org/abs/1711.07356
Towell, G.G., Shavlik, J.W.: Extracting refined rules from knowledge-based neural networks. Mach. Learn. 13(1), 71–101 (1993)
Vanschoren, J., van Rijn, J.N., Bischl, B., Torgo, L.: OpenML: networked science in machine learning. SIGKDD Explor. 15(2), 49–60 (2013). https://doi.org/10.1145/2641190.2641198
Veloso, M.M., Biswas, J., Coltin, B., Rosenthal, S.: CoBots: robust symbiotic autonomous mobile service robots. In: IJCAI, p. 4423 (2015)
Ventocilla, E., et al.: Towards a taxonomy for interpretable and interactive machine learning. In: XAI Workshop on Explainable Artificial Intelligence, pp. 151–157 (2018)
Walter, E., Jaulin, L.: Guaranteed characterization of stability domains via set inversion. IEEE Trans. Autom. Control 39(4), 886–889 (1994). https://doi.org/10.1109/9.286277
Wang, S., Pei, K., Whitehouse, J., Yang, J., Jana, S.: Formal security analysis of neural networks using symbolic intervals. In: 27th USENIX Security Symposium, USENIX Security 2018, Baltimore, MD, USA, 15–17 August 2018, pp. 1599–1614 (2018)
Wellman, H.M., Lagattuta, K.H.: Theory of mind for learning and teaching: the nature and role of explanation. Cogn. Dev. 19(4), 479–497 (2004)
Wen, W., Callahan, J.: Neuralware engineering: develop verifiable ANN-based systems. In: Proceedings IEEE International Joint Symposia on Intelligence and Systems, pp. 60–66. IEEE (1996)
Wen, W., Callahan, J., Napolitano, M.: Towards developing verifiable neural network controller. Technical report (1996)
Wen, W., Callahan, J., Napolitano, M.: Verifying stability of dynamic soft-computing systems. Technical report NASA-IVV-97-002, WVU-CS-TR-97-005, NASA/CR-97-207032, WVU-IVV-97-002 (1997)
Weng, L., et al.: Towards fast computation of certified robustness for ReLU networks. In: Dy, J., Krause, A. (eds.) Proceedings of the 35th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 80, pp. 5276–5285. PMLR, 10–15 July 2018
Xiang, W., Johnson, T.T.: Reachability analysis and safety verification for neural network control systems. CoRR abs/1805.09944 (2018)
Yasmin, M., Sharif, M., Mohsin, S.: Neural networks in medical imaging applications: a survey. World Appl. Sci. J. 22(1), 85–96 (2013)
Acknowledgments
We thank: Nicholay Topin for supporting our spirits at some key junctures of this work; David Held for pointing us to the rl-baselines-zoo repository; David Eckhardt for his proof-reading of earlier versions of this document; the anonymous reviewers for their thoughtful feedback.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Bayani, D., Mitsch, S. (2022). Fanoos: Multi-resolution, Multi-strength, Interactive Explanations for Learned Systems. In: Finkbeiner, B., Wies, T. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2022. Lecture Notes in Computer Science(), vol 13182. Springer, Cham. https://doi.org/10.1007/978-3-030-94583-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-94583-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-94582-4
Online ISBN: 978-3-030-94583-1
eBook Packages: Computer ScienceComputer Science (R0)