Group LARS-Based Iterative Reweighted Least Squares Methodology for Efficient Statistical Modeling of Memory Designs

Regularized logistic regression is a popular classification tool that can be employed to accurately model the binary nature of the memory cell fail mechanisms for purposes of the yield analysis of memory designs. The iterative reweighted least squares (IRLS) method has been employed along with the least angle regression (LARS) to efficiently solve the <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> regularized logistic regression problem. In this brief, we propose an efficient <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> regularized logistic regression methodology. At the core lies a Group LARS-based approach that benefits from Group LARS inherent ability to handle groups of variables and exploits the natural evolution of the solution to speed up the search for the critical features of the classifier. Thus, it tracks Newton’s step direction from one round of the solution to the next and employs weighted directions to efficiently solve for the underlying <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> constrained iterative least squares problem. We apply the methodology in the context of an importance sampling-based yield analysis framework targeting rare fail probability estimation. We study the yield of 14-nm FinFET SRAM designs with programmable and resonant boosting. Our results demonstrate up to <inline-formula> <tex-math notation="LaTeX">$14\times $ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$20\times $ </tex-math></inline-formula> speedup for the Group LARS compared to the pure LARS-based approach, and we report 98.7% accuracy and 0.12 <inline-formula> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> average error compared to pure circuit-simulations approach for the resulting classifier.