Fast statistical analysis of rare circuit failure events via scaled-sigma sampling for high-dimensional variation space

Abstract

Accurately estimating the rare failure rates for nanoscale circuit blocks (e.g., SRAM, DFF, etc.) is a challenging task, especially when the variation space is high-dimensional. In this paper, we propose a novel scaled-sigma sampling (SSS) method to address this technical challenge. The key idea of SSS is to generate random samples from a distorted distribution for which the standard deviation (i.e., sigma) is scaled up. Next, the failure rate is accurately estimated from these scaled random samples by using an analytical model derived from the theorem of "soft maximum". Several circuit examples designed in nanoscale technologies demonstrate that the proposed SSS method achieves superior accuracy over the traditional importance sampling technique when the dimensionality of the variation space is more than a few hundred.

Multiple shift-vector importance sampling method using support vector machine and clustering for high-density DRAM designs

“…, the convergence is immediate [8]. However, since we do not know F a priori, nor do we know p f in (6), h * is not a realistic solution.…”

“…The conventional Monte Carlo (MC) methods require tremendous number of circuit simulations. To address this problem, a number of new statistical algorithms and methodologies have been proposed and developed [3], [5], [6], [8], but most of them focus on the application to SRAM circuits. The DRAM applications, however, require more efficient scaling and integration strategy to address critical challenges caused by huge storage capacitor degradation and aggressive power reduction during each successive generation, for which more efficient statistical methods for failure rate estimation are needed.…”

AutoPrivacy: Automated Layer-wise Parameter Selection for Secure Neural Network Inference

“…However, to simulate a 2 −15 decryption error rate, at least 2 30 brute-force Monte-Carlo runs are required. To reduce simulation overhead, we adopt Sigma-Scaled Sampling [22] to study high dimensional Gaussian random variables. A HE-based linear layer with the initial noise vector e can be abstracted as a function f (e).…”

Correlated Rare Failure Analysis via Asymptotic Probability Evaluation

“…where Δx denotes the volume of a hyper-rectangle and M is the approximation order. In (8) If the number of hyper-rectangles (i.e., M) is sufficiently large, we can obtain an accurate approximation for the integration in (7). For the 2nd order SFR S2 (i.e., the SFR of two cells), we can apply the similar approximation:…”

“…Most of them are based on Important Sampling (IS) [2]- [4] or Boundary Searching (BS) [5]. More recently, Scaled-Sigma Sampling (SSS) [6]- [8] and Subset Simulation (SUS) [9] are proposed to handle large-scale circuits characterized by a high-dimensional variation space involving hundreds of or even thousands of independent random variables.…”