Abstract
Despite the increasing popularity of Machine Learning methods, their usage in safety-critical applications is sometimes limited by the impossibility of providing formal guarantees on their behaviour. In this work we focus on one such application, where Kernel Ridge Regression with Random Fourier Features is used to learn controllers for a prosthetic hand. Due to the non-linearity of the activation function used, these controllers sometimes fail in correctly identifying users’ intention. Under specific circumstances muscular activation levels may be misinterpreted by the method, resulting in the prosthetic hand not behaving as intended. To alleviate this problem, we propose a novel method to verify the presence of this kind of intent detection mismatch and to repair controllers leveraging off-the-shelf LP technology without using additional data. We demonstrate the feasibility of our approach using datasets gathered from human participants.
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- 1.
In practice, the value of \(t_a\) is upper bounded by operating range of EMG sensors.
- 2.
We implemented our procedure using Python version 2.7. and the libraries sklearn and cvxopt for learning and optimization respectively. The default solver of cvxopt, i.e., conelp, was used – see [27] for more details. All the experiments are capped at 10 min of CPU time and 4 GBs of memory; experiments ran on a Ubuntu 18.04 machine equipped with a quad-core i5 Intel CPU running at 2.60 GHz.
- 3.
Notice that for power-grasping \(a_{max}\) is equal to one.
References
Taigman, Y., Yang, M., Ranzato, M., Wolf, L.: DeepFace: closing the gap to human-level performance in face verification. In: CVPR, pp. 1701–1708 (2014)
Yu, D., Hinton, G.E., Morgan, N., Chien, J.-T., Sagayama, S.: Introduction to the special section on deep learning for speech and language processing. IEEE Trans. Audio Speech Lang. Process. 20(1), 4–6 (2012)
LeCun, Y., Bengio, Y., Hinton, G.E.: Deep learning. Nature 521(7553), 436–444 (2015)
Rahimi, A., Recht, B.: Random features for large-scale kernel machines. In: NIPS, pp. 1177–1184 (2008)
Gijsberts, A., Metta, G.: Incremental learning of robot dynamics using random features. In: ICRA, pp. 951–956 (2011)
Fougner, A., Stavdahl, Ø., Kyberd, P.J., Losier, Y.G., Parker, P.A.: Control of upper limb prostheses: terminology and proportional myoelectric control - a review. IEEE Trans. Neural Syst. Rehabil. Eng. 20(5), 663–677 (2012)
Merletti, R., Botter, A., Cescon, C., Minetto, M.A., Vieira, T.M.M.: Advances in surface EMG: recent progress in clinical research applications. Crit. Rev. Biomed. Eng. 38(4), 347–379 (2011)
Gijsberts, A., et al.: Stable myoelectric control of a hand prosthesis using non-linear incremental learning. Front. Neurorobot. 8 (2014)
Strazzulla, I., Nowak, M., Controzzi, M., Cipriani, C., Castellini, C.: Online bimanual manipulation using surface electromyography and incremental learning. IEEE Trans. Neural Syst. Rehabil. Eng. 25(3), 227–234 (2017)
Gestel, T.V., et al.: Benchmarking least squares support vector machine classifiers. Mach. Learn. 54(1), 5–32 (2004)
Patel, G., Nowak, M., Castellini, C.: Exploiting knowledge composition to improve real-life hand prosthetic control. IEEE Trans. Neural Syst. Rehabil. Eng. 25(7), 967–975 (2017)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, Hoboken (1999)
Leofante, F., Narodytska, N., Pulina, L., Tacchella, A.: Automated verification of neural networks: advances, challenges and perspectives. arXiv preprint arXiv:1805.09938 (2018)
Narodytska, N., Kasiviswanathan, S.P., Ryzhyk, L., Sagiv, M., Walsh, T.: Verifying properties of binarized deep neural networks. In: AAAI, pp. 6615–6624 (2018)
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
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. LNCS, vol. 10426, pp. 97–117. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_5
Leofante, F., Tacchella, A.: Learning in physical domains: mating safety requirements and costly sampling. In: Adorni, G., Cagnoni, S., Gori, M., Maratea, M. (eds.) AI*IA 2016. LNCS (LNAI), vol. 10037, pp. 539–552. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49130-1_39
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
Fischetti, M., Jo, J.: Deep neural networks and mixed integer linear optimization. Constraints 23(3), 296–309 (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
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: 2018 IEEE Symposium on Security and Privacy (SP) (2018)
Valero-Cuevas, F.J.: Predictive modulation of muscle coordination pattern magnitude scales fingertip force magnitude over the voluntary range. J. Neurophysiol. 83(3), 1469–1479 (2000)
Poston, B., Danna-Dos Santos, A., Jesunathadas, M., Hamm, T.M., Santello, M.: Force-independent distribution of correlated neural inputs to hand muscles during three-digit grasping. J. Neurophysiol. 104(2), 1141–1154 (2010)
de Rugy, A., Loeb, G.E., Carroll, T.J.: Muscle coordination is habitual rather than optimal. J. Neurosci. 32(21), 7384–7391 (2012)
He, J., Zhang, D., Sheng, X., Li, S., Zhu, X.: Invariant surface emg feature against varying contraction level for myoelectric control based on muscle coordination. IEEE J. Biomed. Heal. Inform. 19(3), 874–882 (2015)
Al-Timemy, A.H., Khushaba, R.N., Bugmann, G., Escudero, J.: Improving the performance against force variation of emg controlled multifunctional upper-limb prostheses for transradial amputees. IEEE Trans. Neural Syst. Rehabil. Eng. 24(6), 650–661 (2016)
Vandenberghe, L.: The CVXOPT linear and quadratic cone program solvers (2010)
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Guidotti, D., Leofante, F., Castellini, C., Tacchella, A. (2019). Repairing Learned Controllers with Convex Optimization: A Case Study. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_24
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