high sigma analysis - university of california, los...

High Sigma Analysis

Outline

• Preliminary of High Sigma Analysis

• A Fast and Provably Bounded Failure Analysis of Memory Circuits in High Dimensions

• Hyperspherical Clustering and Sampling for Rare Event Analysis with Multiple Failure Region Coverage

• REscope: High-dimensional Statistical Circuit Simulation towards Full Failure Region Coverage

High Sigma Analysis

High Sigma Analysis

High Sigma Analysis

Basic Idea in Importance Sampling

The Proposed Method

Stage2: Choosing Mean and Sigma for Yt

Stage3: Evaluation of Conditional Probability

High Sigma Analysis

High Sigma Analysis

High Sigma Analysis

Hyperspherical clustering and sampling (HSCS)

• Phase 1: Hyperspherical clustering: identify multiple failure regions

• Iteratively update cluster centroid

• Samples are associated with different weight during clustering

• Cluster centroid are biased to more important samples (with higher weights)

High Sigma Analysis

High Sigma Analysis

Another alternative

• Presampling: sketch the circuit behavior

• Parameter pruning: each parameter is analyzed in terms of how sensitive it is to cause a circuit failure.

ReliefF specifically looks at the sensitivity around the decision boundary

Another alternative

• Classification: relies on support vector machine (SVM) with Guassianradial basis function (RBF) kernel to identify failure regions and to train and classify samples. It is also a classification method to co-recognize the multiple failure regions.