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NOFIS: Normalizing Flow for Rare Circuit Failure Analysis

Published: 07 November 2024 Publication History

Abstract

Accurate estimation of rare failure occurrence probability is crucial for ensuring the proper and reliable functioning of integrated circuits (ICs). Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this problem and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as 10 quantitative experiments, which highlight NOFIS's superior accuracy over baseline approaches.

References

[1]
Siu-Kui Au and James L Beck. 2001. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic engineering mechanics 16, 4 (2001), 263--277.
[2]
A.J. Bhavnagarwala, Xinghai Tang, and J.D. Meindl. 2001. The impact of intrinsic device fluctuations on CMOS SRAM cell stability. IEEE Journal of Solid-State Circuits 36, 4 (2001), 658--665.
[3]
Gino Biondini. 2015. An introduction to rare event simulation and importance sampling. In Handbook of Statistics. Vol. 33. Elsevier, 29--68.
[4]
James Antonio Bucklew and J Bucklew. 2004. Introduction to rare event simulation. Vol. 5. Springer.
[5]
Laurent Dinh, David Krueger, and Yoshua Bengio. 2014. Nice: Non-linear independent components estimation. arXiv preprint arXiv:1410.8516 (2014).
[6]
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. 2016. Density estimation using Real NVP. In International Conference on Learning Representations.
[7]
Lara Dolecek, Masood Qazi, Devavrat Shah, and Anantha Chandrakasan. 2008. Breaking the simulation barrier: SRAM evaluation through norm minimization. In 2008 IEEE/ACM International Conference on Computer-Aided Design. IEEE, 322--329.
[8]
Zhengqi Gao, Jun Tao, Yangfeng Su, Dian Zhou, Xuan Zeng, and Xin Li. 2020. Efficient Rare Failure Analysis Over Multiple Corners via Correlated Bayesian Inference. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39, 10 (2020), 2029--2041.
[9]
Zhengqi Gao, Jun Tao, Fan Yang, Yangfeng Su, Dian Zhou, and Xuan Zeng. 2019. Efficient Performance Trade-off Modeling for Analog Circuit based on Bayesian Neural Network. In 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). 1--8.
[10]
Rouwaida Kanj, Rajiv Joshi, and Sani Nassif. 2006. Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events. In Proceedings of the 43rd Design Automation Conference. 69--72.
[11]
Kentaro Katayama, Shiho Hagiwara, Hiroshi Tsutsui, Hiroyuki Ochi, and Takashi Sato. 2010. Sequential importance sampling for low-probability and high-dimensional SRAM yield analysis. In 2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). 703--708.
[12]
S. Mukhopadhyay, H. Mahmoodi, and K. Roy. 2004. Statistical design and optimization of SRAM cell for yield enhancement. In IEEE/ACM International Conference on Computer Aided Design. 10--13.
[13]
George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan. 2021. Normalizing flows for probabilistic modeling and inference. The Journal of Machine Learning Research 22, 1 (2021), 2617--2680.
[14]
Xiao Shi, Fengyuan Liu, Jun Yang, and Lei He. 2018. A fast and robust failure analysis of memory circuits using adaptive importance sampling method. In Proceedings of the 55th Design Automation Conference. 1--6.
[15]
Xiao Shi, Hao Yan, Qiancun Huang, Jiajia Zhang, Longxing Shi, and Lei He. 2019. Meta-Model Based High-Dimensional Yield Analysis Using Low-Rank Tensor Approximation. In Proceedings of the 56th Design Automation Conference 2019.
[16]
Xiao Shi, Hao Yan, Chuwen Li, Jianli Chen, Longxing Shi, and Lei He. 2020. A Non-Gaussian Adaptive Importance Sampling Method for High-Dimensional and Multi-Failure-Region Yield Analysis. In Proceedings of the 39th International Conference on Computer-Aided Design.
[17]
Amith Singhee and Rob A. Rutenbar. 2009. Statistical Blockade: Very Fast Statistical Simulation and Modeling of Rare Circuit Events and Its Application to Memory Design. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 28, 8 (2009), 1176--1189.
[18]
Jingwen Song, Pengfei Wei, Marcos Valdebenito, and Michael Beer. 2021. Active learning line sampling for rare event analysis. Mechanical Systems and Signal Processing 147 (2021), 107113.
[19]
Shupeng Sun and Xin Li. 2014. Fast statistical analysis of rare circuit failure events via subset simulation in high-dimensional variation space. In 2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). 324--331.
[20]
Shupeng Sun, Xin Li, Hongzhou Liu, Kangsheng Luo, and Ben Gu. 2015. Fast statistical analysis of rare circuit failure events via scaled-sigma sampling for high-dimensional variation space. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 34, 7 (2015), 1096--1109.
[21]
Jun Tao, Handi Yu, Dian Zhou, Yangfeng Su, Xuan Zeng, and Xin Li. 2017. Correlated rare failure analysis via Asymptotic Probability Evaluation. In 2017 54th ACM/EDAC/IEEE Design Automation Conference (DAC). 1--6.
[22]
Zushu Yan, Pui-In Mak, Man-Kay Law, and Rui Martins. 2012. A 0.016mm2 144uW three-stage amplifier capable of driving 1-to-15nF capacitive load with >0.95MHz GBW. In 2012 IEEE International Solid-State Circuits Conference. 368--370.
[23]
Handi Yu, Jun Tao, Changhai Liao, Yangfeng Su, Dian Zhou, Xuan Zeng, and Xin Li. 2016. Efficient statistical analysis for correlated rare failure events via Asymptotic Probability Approximation. In 2016 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). 1--8.

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    cover image ACM Conferences
    DAC '24: Proceedings of the 61st ACM/IEEE Design Automation Conference
    June 2024
    2159 pages
    ISBN:9798400706011
    DOI:10.1145/3649329
    This work is licensed under a Creative Commons Attribution International 4.0 License.

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    Published: 07 November 2024

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    1. rare circuit failure
    2. importance sampling
    3. normalizing flows

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    DAC '24: 61st ACM/IEEE Design Automation Conference
    June 23 - 27, 2024
    CA, San Francisco, USA

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