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Main sources of variability and non-determinism in AD software: taxonomy and prospects to handle them

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Abstract

Safety standards in domains like automotive and avionics seek for deterministic execution (lack of jittery behavior) as a stepping stone to build a certification argument on the correct timing behavior of the system. However, the use of artificial-intelligence (AI) software in safety-critical systems carries several built-in and derivative sources of non-determinism that are at odds with safety standard determinism requirements. In this work we analyze the main sources of non-determinism of autonomous driving (AD) software, as highly representative and compelling example of the use of AI software, deep neural networks (DNN) in particular, in critical embedded systems. Paradoxically, DNN-based software in its inference phase—once the NN structure and weights have been fixed—turns out to consist mainly in matrix multiplications, which are inherently quite time deterministic. Our work focuses on sources of variability and non-determinism in AD software, covering algorithmic elements of AD software, low-level software and hardware computing platform, and data-flow constraints among AD modules. As final contribution of our work, which mainly focuses on problem identification, we develop some prospects on the information and metrics needed to better understand and control the unpredictability and non-determinism of AD software.

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Data availability statement

The data supporting the results reported in this work are available from the authors upon reasonable request.

Notes

  1. We use the terms Deep Learning (DL) and Neural Network (NN) indistinctly.

  2. Note that the standard notation in probability p denotes that it is a probability mass function, while P is a probability measure.

  3. Note that while the impact of such scenario depends on the application semantics, it is arising without breaking P timing bounds.

References

  • Aghilinasab H, Ali W, Yun H, Pellizzoni R (2020) Dynamic memory bandwidth allocation for real-time GPU-based SoC platforms. IEEE Trans Comput Aid Des Integr Circ Syst. https://doi.org/10.1109/TCAD.2020.3012210

    Article  Google Scholar 

  • Alahi A, Goel K, Ramanathan V, Robicquet A, Fei-Fei L, Savarese S (2016) Social LSTM: human trajectory prediction in crowded spaces. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 961–971

  • Albawi S, Mohammed TA, Al-Zawi S (2017) Understanding of a convolutional neural network. In: 2017 international conference on engineering and technology (ICET), IEEE, pp. 1–6

  • Alcon M, Tabani H, Kosmidis L, Mezzetti E, Abella J, Cazorla FJ (2020) Timing of autonomous driving software: problem analysis and prospects for future solutions. In: 2020 IEEE real-time and embedded technology and applications symposium (RTAS), pp. 267–280. https://doi.org/10.1109/RTAS48715.2020.000-1

  • Alcon M, Tabani H, Kosmidis L, Mezzetti E, Abella J, Cazorla FJ (2020) Timing of autonomous driving software: Problem analysis and prospects for future solutions. In: RTAS, pp. 267–280

  • Alloghani M, Al-Jumeily D, Mustafina J, Hussain A, Aljaaf AJ (2020) A systematic review on supervised and unsupervised machine learning algorithms for data science. Supervised and unsupervised learning for data science, 3–21

  • Al-Qizwini M, Barjasteh I, Al-Qassab H, Radha H (2017) Deep learning algorithm for autonomous driving using googlenet. In: 2017 IEEE intelligent vehicles symposium (IV). IEEE, pp. 89–96

  • Apex.AI: Apex.OS (2023) An end-to-end operating system for mobility, smart machines and IoT. https://www.apex.ai/apex-os Accessed Mar 2023

  • ApolloAuto (2018) Apollo 3.0 software architecture. https://github.com/ApolloAuto/apollo/blob/master/docs/specs/Apollo_3.0_Software_Architecture.md Accessed May 2019

  • ApolloAuto (2021) CyberRT. https://github.com/ApolloAuto/apollo/tree/master/cyber. https://github.com/ApolloAuto/apollo/tree/master/cyber. Accessed June 2022

  • ApolloAuto (2022) Perception. https://github.com/ApolloAuto/apollo/tree/r5.0.0/modules/perception Accessed Nov 2022

  • ARINC Inc. (2012) ARINC specification 653: avionics application software standard standard interface. ARINC Inc

  • Arm (2017a) ARM CoreLink QoS-400 network interconnect advanced quality of service supplement to ARM CoreLink NIC-400 network interconnect technical reference manual

  • Arm (2017b) ARM CoreLink QVN-400 network interconnect advanced quality of service using virtual networks supplement to ARM CoreLink NIC-400 network interconnect technical reference manual

  • Arm (2022) Arm ® architecture reference manual supplement memory system resource partitioning and monitoring (MPAM), for Armv8-A

  • Ashukha A, Lyzhov A, Molchanov D, Vetrov D (2020) Pitfalls of in-domain uncertainty estimation and ensembling in deep learning. arXiv preprint arXiv:2002.06470

  • Axer P, Ernst R, Falk H, Girault A, Grund D, Guan N, Jonsson B, Marwedel P, Reineke J, Rochange C, Sebastian M, von Hanxleden R, Wilhelm R, Yi W (2014) Building timing predictable embedded systems. ACM Trans Embed Comput Syst 13(4):82–18237

    Article  Google Scholar 

  • Baidu (2018) Apollo, an open autonomous driving platform. http://apollo.auto/

  • Becker M, Nikolic B, Dasari D, Akesson B, Nélis V, Behnam M, Nolte T (2017) Partitioning and analysis of the network-on-chip on a cots many-core platform. In: 2017 IEEE real-time and embedded technology and applications symposium (RTAS), pp. 101–112. https://doi.org/10.1109/RTAS.2017.32

  • Belluardo L, Stevanato A, Casini D, Cicero G, Biondi A, Buttazzo G (2021) A multi-domain software architecture for safe and secure autonomous driving. In: 2021 IEEE 27th international conference on embedded and real-time computing systems and applications (RTCSA), pp. 73–82. https://doi.org/10.1109/RTCSA52859.2021.00017

  • Biondi A, Di Natale M (2018) Achieving predictable multicore execution of automotive applications using the LET paradigm. In: 2018 IEEE real-time and embedded technology and applications symposium (RTAS). IEEE, pp. 240–250

  • Bishop CM (1994) Mixture density networks

  • Blaß T, Casini D, Bozhko S, Brandenburg BB (2021) A ROS 2 response-time analysis exploiting starvation freedom and execution-time variance. In: RTSS, pp. 41–53

  • Blundell C, Cornebise J, Kavukcuoglu K, Wierstra D (2015) Weight uncertainty in neural network. In: International conference on machine learning. PMLR, pp. 1613–1622

  • Brando A (2022) Aleatoric uncertainty modelling in regression problems using deep learning

  • Brando A, Rodriguez JA, Vitria J, Rubio Muñoz A (2019) Modelling heterogeneous distributions with an uncountable mixture of asymmetric laplacians. Adv Neural Inf Process Syst 32

  • Brando A, Rodríguez-Serrano JA, Ciprian M, Maestre R, Vitrià J (2018) Uncertainty modelling in deep networks: forecasting short and noisy series. In: Joint European conference on machine learning and knowledge discovery in databases. Springer, pp. 325–340

  • Brando A, Serra I, Mezzetti E, Abella J, Cazorla FJ (2022) Using quantile regression in neural networks for contention prediction in multicore processors. In: 34th Euromicro conference on real-time systems (ECRTS 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik

  • Brando A, Serra I, Mezzetti E, Abella J, Cazorla FJ (2023) Standardizing the probabilistic sources of uncertainty for the sake of safety deep learning. In: AAAI’s workshop on AI safety

  • Cardona J, Hernández C, Abella J, Cazorla FJ (2019) Maximum-contention control unit (MCCU): resource access count and contention time enforcement. In: Design, automation & test in Europe conference & exhibition, DATE, pp. 710–715. https://doi.org/10.23919/DATE.2019.8715155

  • Cardona J, Hernandez C, Mezzetti E, Abella J, Cazorla FJ (2018) NoCo: ILP-based worst-case contention estimation for mesh real-time many cores. In: 2018 IEEE real-time systems symposium (RTSS). https://doi.org/10.1109/rtss.2018.00043

  • Certification Authorities Software Team (2016) CAST-32A multi-core processors

  • Certification authorities software team (2016, Nov) Multi-core processors—position paper. Technical report, CAST-32A

  • Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geosci Model Dev 7(3):1247–1250

    Article  Google Scholar 

  • Cheon K, Kim J, Hamadache M, Lee D (2015) On replacing PID controller with deep learning controller for DC motor system. J Autom Control Eng 3:452–456. https://doi.org/10.12720/joace.3.6.452-456

    Article  Google Scholar 

  • Chisholm M, Kim N, Ward BC, Otterness N, Anderson JH, Smith FD (2016) Reconciling the tension between hardware isolation and data sharing in mixed-criticality, multicore systems. In: RTSS, pp. 57–68

  • Crespo, A., Ripoll, I., Masmano, M. (2010) Partitioned embedded architecture based on hypervisor: the XtratuM approach. In: European dependable computing conference (EDCC), pp. 67–72. https://doi.org/10.1109/EDCC.2010.18

  • Dabney W, Rowland M, Bellemare M, Munos R (2018) Distributional reinforcement learning with quantile regression. In: Proceedings of the AAAI conference on artificial intelligence, vol. 32

  • Dasari D, Nelis V (2012) An analysis of the impact of bus contention on the wcet in multicores. In: Proceedings of the 2012 IEEE 14th international conference on high performance computing and communication. HPCC ’12, pp. 1450–1457. https://doi.org/10.1109/HPCC.2012.212

  • Der Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105–112

    Article  Google Scholar 

  • Díaz E, Mezzetti E, Kosmidis L, Abella J, Cazorla FJ (2018) Modelling multicore contention on the aurixtm tc27x. In: Proceedings of the 55th annual design automation conference, DAC 2018, San Francisco, CA, USA, June 24–29, 2018

  • Dogan Ü, Edelbrunner J, Iossifidis I (2011) Autonomous driving: a comparison of machine learning techniques by means of the prediction of lane change behavior. In: 2011 IEEE international conference on robotics and biomimetics. IEEE, pp. 1837–1843

  • Dürr M, von der Brüggen G, Chen K, Chen J (2019) End-to-end timing analysis of sporadic cause-effect chains in distributed systems. ACM Trans Embed Comput Syst 18(5s):58–15824

    Article  Google Scholar 

  • EASA (2022) FAE general acceptable means of compliance for airworthiness of products, parts and appliances (AMC-20). Amendment 23. Annex I to ED decision 2022/001/R. AMC 20-193 use of multi-core processors. Technical report, EASA

  • Electronics L (2022) SVL simulator: an end-to-end autonomous vehicle simulation platform. https://www.svlsimulator.com/ Accessed Nov 2022

  • Falk R, Jörg S (2016) Software mechanisms for controlling QoS. In: 2021 design, automation & test in Europe conference & exhibition, DATE 2021, virtual conference, 1–5 Feb 2021, pp. 1485–1488

  • Farshchi F, Huang Q, Yun H (2020) BRU: bandwidth regulation unit for real-time multicore processors. In: IEEE real-time and embedded technology and applications symposium, RTAS 2020, Sydney, Australia, April 21–24, 2020, pp. 364–375. https://doi.org/10.1109/RTAS48715.2020.00011

  • Feiertag N, Richter K, Nordlander J, Jonsson J (2008) A compositional framework for end-to-end path delay calculation of automotive systems under different path semantics. In: RTSS—workshop on compositional theory and technology for real-time embedded systems, pp. 41–53

  • Feng D, Rosenbaum L, Dietmayer K (2018) Towards safe autonomous driving: capture uncertainty in the deep neural network for lidar 3D vehicle detection. In: 2018 21st international conference on intelligent transportation systems (ITSC). IEEE, pp. 3266–3273

  • Foundation TA Autoware (2016) An open autonomous driving platform. https://github.com/CPFL/Autoware/

  • Gaide B, Gaitonde D, Ravishankar C, Bauer T (2019) Xilinx adaptive compute acceleration platform: Versaltm architecture. FPGA ’19. Association for Computing Machinery, New York, pp. 84–93. https://doi.org/10.1145/3289602.3293906

  • Gal Y, Ghahramani Z (2016) Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In: International conference on machine learning. PMLR, pp. 1050–1059

  • Gawlikowski J, Tassi CRN, Ali M, Lee J, Humt M, Feng J, Kruspe A, Triebel R, Jung P, Roscher R, et al (2021) A survey of uncertainty in deep neural networks. arXiv preprint arXiv:2107.03342

  • Gracioli G, Fröhlich AA (2015) On the design and evaluation of a real-time operating system for cache-coherent multicore architectures. ACM SIGOPS Oper Syst Rev 49(2):2–16

    Article  Google Scholar 

  • Gracioli G, Alhammad A, Mancuso R, Fröhlich AA, Pellizzoni R (2015) A survey on cache management mechanisms for real-time embedded systems. ACM Comput Surv 48(2):36, 32. https://doi.org/10.1145/2830555

    Article  Google Scholar 

  • Grigorescu S, Trasnea B, Cocias T, Macesanu G (2020) A survey of deep learning techniques for autonomous driving. J Field Robot 37(3):362–386

    Article  Google Scholar 

  • Guo C, Pleiss G, Sun Y, Weinberger KQ (2017) On calibration of modern neural networks. In: International conference on machine learning. PMLR, pp. 1321–1330

  • Hamuda E, Mc Ginley B, Glavin M, Jones E (2018) Improved image processing-based crop detection using Kalman filtering and the Hungarian algorithm. Comput Electron Agric 148:37–44

    Article  Google Scholar 

  • Hassan M, Pellizzoni R (2018) Bounding DRAM interference in COTS heterogeneous MPSOCS for mixed criticality systems. IEEE Trans Comput Aided Des Integr Circ Syst 37:11

    Article  Google Scholar 

  • Hüllermeier E (2022) Quantifying aleatoric and epistemic uncertainty in machine learning: are conditional entropy and mutual information appropriate measures? arXiv preprint arXiv:2209.03302

  • Hüllermeier E, Waegeman W (2021) Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods. Mach Learn 110(3):457–506

    Article  MathSciNet  MATH  Google Scholar 

  • Huseljic D, Sick B, Herde M, Kottke D (2021) Separation of aleatoric and epistemic uncertainty in deterministic deep neural networks. In: 2020 25th international conference on pattern recognition (ICPR). IEEE, pp. 9172–9179

  • International Organization for Standardization (2009) ISO/DIS 26262. Road vehicles—functional safety

  • International Organization for Standardization (2019) ISO/PAS 21448. Road vehicles—safety of the intended functionality

  • Jalle J, Abella J, Quiñones E, Fossati L, Zulianello M, Cazorla FJ (2014) AHRB: a high-performance time-composable AMBA AHB bus. In: 20th IEEE real-time and embedded technology and applications symposium, RTAS 2014, Berlin, Germany, April 15–17, 2014

  • Kang E, Huang L (2018)Probabilistic analysis of timing constraints in autonomous automotive systems using simulink design verifier. In: SETTA: lecture notes in computer science, vol. 10998, pp. 170–186

  • Kendall A, Gal Y (2017) What uncertainties do we need in Bayesian deep learning for computer vision? arXiv preprint arXiv:1703.04977

  • Kendall A, Gal Y, Cipolla R (2018) Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 7482–7491

  • Kuutti S, Bowden R, Jin Y, Barber P, Fallah S (2020) A survey of deep learning applications to autonomous vehicle control. IEEE Trans Intell Transp Syst 22(2):712–733

    Article  Google Scholar 

  • Lakshminarayanan B, Pritzel A, Blundell C (2017) Simple and scalable predictive uncertainty estimation using deep ensembles. Adv Neural Inf Process Syst 30

  • LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  • Lee S (2003) Real-time wormhole channels. J Parallel Distrib Comput 63:299–311

    Article  MATH  Google Scholar 

  • Li Z, Hasegawa A, Azumi T (2022) Autoware_perf: a tracing and performance analysis framework for ROS 2 applications. J Syst Archit 123:102341

    Article  Google Scholar 

  • Liang M, Hu X (2015) Recurrent convolutional neural network for object recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3367–3375

  • Lippiello V, Siciliano B, Villani L (2007) Adaptive extended Kalman filtering for visual motion estimation of 3D objects. Control Eng Pract 15(1):123–134

    Article  Google Scholar 

  • Lynx (2020) Challenges building safe multicore systems. https://www.lynx.com/embedded-systems-learning-center/challenges-building-safe-multicore-mcp-software-systems

  • LYNX software technologies: LynxSecure separation kernel hypervisor (2022)

  • Macenski S, Foote T, Gerkey BP, Lalancette C, Woodall W (2022) Robot operating system 2: design, architecture, and uses in the wild. Sci Robot 7:66. https://doi.org/10.1126/scirobotics.abm6074

    Article  Google Scholar 

  • MacKay DJ (1995) Bayesian neural networks and density networks. Nucl Inst Methods Phys Res Sect A 354(1):73–80

    Article  Google Scholar 

  • Mittal S (2017) A survey of techniques for cache partitioning in multicore processors. ACM Comput Surv 50(2):27–12739. https://doi.org/10.1145/3062394

    Article  Google Scholar 

  • Moshayedi AJ, Roy AS, Kolahdooz A, Shuxin Y (2022) Deep learning application pros and cons over algorithm. EAI Endorsed Trans AI Robot. https://doi.org/10.4108/airo.v1i.19

    Article  Google Scholar 

  • Mubeen S, Nolte T (2015) Applying end-to-end path delay analysis to multi-rate automotive systems developed using legacy tools. IEEE international workshop on factory communication systems—proceedings, WFCS 2015. https://doi.org/10.1109/WFCS.2015.7160585

  • Murphy KP (2012) Machine learning—a probabilistic perspective. Adaptive computation and machine learning series

  • NimbleAI consortium (n.d.) NimbleAI: ultra-energy efficient and secure neuromorphic sensing and processing at the endpoint. https://www.nimbleai.eu/

  • Nowotsch J, Paulitsch M, Buhler D, Theiling H, Wegener S, Schmidt M (2014) Multi-core interference-sensitive WCET analysis leveraging runtime resource capacity enforcement. In: 26th Euromicro conference on real-time systems. ECRTS

  • NVIDIA (2022) NVIDIA Orin series system-on-chip. Technical Reference Manual. v1.0p

  • NVIDIA (2023) NVIDIA DRIVE Hyperion 7.1. https://developer.nvidia.com/drive/hyperion-7.1. Accessed Mar 2023

  • Oliphant T (2006) NumPy: a guide to NumPy. USA: Trelgol Publishing. http://www.numpy.org/

  • Pagani M, Rossi E, Biondi A, Marinoni M, Lipari G, Buttazzo GC (2019) A bandwidth reservation mechanism for AXI-based hardware accelerators on fpgas. In: 31st Euromicro conference on real-time systems, Vol. 133, ECRTS 2019, July 9–12, 2019. Stuttgart, Germany: LIPIcs

  • Pellizzoni R, Betti E, Bak S, Yao G, Criswell J, Caccamo M, Kegley R (2011) A predictable execution model for cots-based embedded systems. In: 2011 17th IEEE real-time and embedded technology and applications symposium, pp. 269–279. https://doi.org/10.1109/RTAS.2011.33

  • Pellizzoni R, Bui BD, Caccamo M, Sha L (2008) Coscheduling of cpu and i/o transactions in cots-based embedded systems. In: 2008 real-time systems symposium, pp. 221–231. https://doi.org/10.1109/RTSS.2008.42

  • Peng Z, Yang J, Chen T-H, Ma L (2020) A first look at the integration of machine learning models in complex autonomous driving systems: a case study on apollo. In: Proceedings of the 28th ACM joint meeting on european software engineering conference and symposium on the foundations of software engineering, pp. 1240–1250

  • Pishro-Nik H (2020) Mean squared error (MSE). https://shorturl.at/tFGY4. Accessed 19 Sept 2020

  • Qian Y, Lu Z, Dou W (2009) Analysis of worst-case delay bounds for best-effort communication in wormhole networks on chip. In: 2009 3rd ACM/IEEE international symposium on networks-on-chip. IEEE, pp. 44–53

  • Quigley et al (2009) M ROS: an open-source robot operating system. ICRA Workshop on Open Source Software

    Google Scholar 

  • Redmon J, Divvala S, Girshick R, Farhadi A (2016) You only look once: Unified, real-time object detection. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 779–788

  • Restuccia F, Pagani M, Biondi A, Marinoni M, Buttazzo G (2019) Is your bus arbiter really fair? Restoring fairness in AXI interconnects for FPGA SoCs. ACM Trans Embedded Comput Syst 18(5s):51–15122. https://doi.org/10.1145/3358183

    Article  Google Scholar 

  • Restuccia F, Biondi A (2021) Time-predictable acceleration of deep neural networks on FPGA SOC platforms. In: 2021 IEEE real-time systems symposium (RTSS), pp. 441–454. https://doi.org/10.1109/RTSS52674.2021.00047

  • RTI: RTI Connext Drive (2023) The leading safety-certified data-centric communications framework for software-defined vehicles. https://www.rti.com/drive Accessed Mar 2023

  • Saito Y, Sato F, Azumi T, Kato S, Nishio N (2018) ROSCH: real-time scheduling framework for ROS. In: RTCSA, pp. 52–58

  • Scheffer T, Decomain C, Wrobel S (2001) Active hidden Markov models for information extraction. In: International symposium on intelligent data analysis. Springer, pp. 309–318

  • Schlatow J, Ernst R (2016) Response-time analysis for task chains in communicating threads. In: 2016 IEEE real-time and embedded technology and applications symposium (RTAS), Vienna, Austria, April 11–14, 2016, pp. 245–254. https://doi.org/10.1109/RTAS.2016.7461359

  • Schliecker S, Negrean M, Ernst R (2010) Bounding the shared resource load for the performance analysis of multiprocessor systems. In: Proceedings of the conference on design, automation and test in Europe. DATE ’10, pp. 759–764

  • Schoeberl M, Abbaspour S, Akesson B, Audsley NC, Capasso R, Garside J, Goossens K, Goossens S, Hansen S, Heckmann R, Hepp S, Huber B, Jordan A, Kasapaki E, Knoop J, Li Y, Prokesch D, Puffitsch W, Puschner PP, Rocha A, Silva C, Sparsø J, Tocchi A (2015) T-CREST: time-predictable multi-core architecture for embedded systems. J Syst Archit 61(9):449–471

    Article  Google Scholar 

  • Sciangula G, Restuccia F, Biondi A, Buttazzo G (2022) Hardware acceleration of deep neural networks for autonomous driving on FPGA-based SOC. In: 2022 25th Euromicro conference on digital system design (DSD), pp. 406–414. https://doi.org/10.1109/DSD57027.2022.00061

  • Serrano-Cases A, Reina JM, Abella J, Mezzetti E, Cazorla FJ (2021) Leveraging hardware QOS to control contention in the xilinx zynq ultrascale+ MPSOC. In: 33rd Euromicro conference on real-time systems, ECRTS 2021, July 5–9, 2021, Virtual Conference. LIPIcs, vol. 196, pp. 3–1326. https://doi.org/10.4230/LIPIcs.ECRTS.2021.3

  • Shaker MH, Hüllermeier E (2020) Aleatoric and epistemic uncertainty with random forests. In: International symposium on intelligent data analysis. Springer, pp. 444–456

  • Siemens (2022) Jailhouse hypervisor. https://github.com/siemens/jailhouse. Accessed 24-Feb-2022

  • Smola A, Vishwanathan S (2008) Introduction to machine learning. Cambridge University

    Google Scholar 

  • Sohal P, Tabish R, Drepper U, Mancuso R (2020) E-WarP: a system-wide framework for memory bandwidth profiling and management. In: RTSS

  • Sysgo (2021) PikeOS product overview. https://www.sysgo.com/fileadmin/user_upload/data/flyers_brochures/SYSGO_PikeOS_Product_Overview.pdf

  • Tabani H, Pujol R, Abella J, Cazorla FJ (2020) A cross-layer review of deep learning frameworks to ease their optimization and reuse. In: 2020 IEEE 23rd international symposium on real-time distributed computing (ISORC), pp. 144–145. https://doi.org/10.1109/isorc49007.2020.00030

  • Tagasovska N, Lopez-Paz D (2019) Single-model uncertainties for deep learning. Adv Neural Inf Process Syst 32

  • Taud H, Mas J (2018) Multilayer perceptron (MLP). In: Geomatic approaches for modeling land change scenarios, pp. 451–455

  • Templeton B Baidu Unveils Ambitious Robotaxi plan in China (2022). https://www.forbes.com/sites/bradtempleton/2022/11/30/baidu-unvails-ambitious-robotaxi-plan-in-china/ Accessed Mar 2023

  • Tobuschat S, Ernst R (2017) Real-time communication analysis for networks-on-chip with backpressure. In: Design, automation & test in Europe conference & exhibition (DATE), pp. 590–595. https://doi.org/10.23919/date.2017.7927055

  • Vault M (2020) List of probability and statistics symbols. https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/. Accessed 26 May 2020

  • Vilardell S, Serra I, Mezzetti E, Abella J, Cazorla FJ, del Castillo J (2022) Using Markov’s inequality with power-of-k function for probabilistic wcet estimation. In: 34th Euromicro conference on real-time systems (ECRTS 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik

  • Willmott CJ, Matsuura K (2005) Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim Res 30(1):79–82

    Article  Google Scholar 

  • XILINX (2019) Zynq UltraScale+ Device. Technical reference manual. UG1085 (v2.1)

  • Yun H, Mancuso R, Wu ZP, Pellizzoni R (2014) PALLOC: DRAM bank-aware memory allocator for performance isolation on multicore platforms. In: RTAS, pp. 155–166

  • Yun H, Yao G, Pellizzoni R, Caccamo M, Sha L (2013) Memguard: memory bandwidth reservation system for efficient performance isolation in multi-core platforms. In: 19th IEEE real-time and embedded technology and applications symposium, RTAS, pp. 55–64

  • Zeng H, Natale MD, Giusto P, Sangiovanni-Vincentelli AL (2010) Using statistical methods to compute the probability distribution of message response time in controller area network. IEEE Trans Ind Inf 6(4):678–691

    Article  Google Scholar 

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Funding

This work has been supported by the Spanish Ministry of Science and Innovation under grant PID2019-107255GBC21/AEI/10.13039/501100011033, and the European Research Council (ERC) grant agreement No. 772773 (SuPerCom).

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Alcon, M., Brando, A., Mezzetti, E. et al. Main sources of variability and non-determinism in AD software: taxonomy and prospects to handle them. Real-Time Syst 59, 438–478 (2023). https://doi.org/10.1007/s11241-023-09405-1

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