HOLMES: In-Context Failure-Center Localization for High-Dimensional Yield Estimation
HOLMES achieves 5.9% error in high-dimensional settings with a 58.8x speedup.
Key Findings
Methodology
HOLMES reformulates failure-center localization as few-shot binary classification, using TabPFN for gradient-free inference. It combines an SVD-based anisotropic proposal with a hit-rate-driven adaptive mixing scheme to stabilize importance weights.
Key Results
- HOLMES maintains within 5.9% error across five configurations from D=108 to D=1152 in 6T SRAM benchmarks, achieving up to 58.8x speedup over Monte Carlo.
- Compared to the strongest baseline, HOLMES achieves 0.1% and 5.9% error at D=864 and D=1152, while PCA+MNIS records 5.67% and 12.50% error.
- Replacing TabPFN with conventional classifiers results in 28.7% to 73.8% error at D=864, whereas HOLMES achieves only 0.1%.
Significance
HOLMES effectively addresses the accuracy collapse in high-dimensional failure-center localization, significantly improving the efficiency and accuracy of high-sigma yield estimation. It offers a new approach to handling extreme class imbalance, particularly beneficial in SRAM design.
Technical Contribution
HOLMES redefines failure-center localization as few-shot classification, avoiding the ill-posed training loop in traditional methods. Its SVD proposal and hit-rate-driven adaptive mixing scheme provide new theoretical guarantees and engineering possibilities.
Novelty
HOLMES is the first to reformulate failure-center localization as few-shot classification, significantly differing from existing regression or parametric fitting approaches, offering a more robust solution.
Limitations
- In extreme high-dimensional settings, HOLMES may face challenges in feature selection, affecting model generalization.
- In some configurations, hit-rate parameters may need adjustment to ensure stability.
Future Work
Future directions include optimizing feature selection strategies to further enhance performance in high-dimensional settings and exploring HOLMES's potential applications in other domains.
AI Executive Summary
As SRAM arrays scale to advanced technology nodes, process variations push circuit performance beyond specifications, making yield estimation a critical bottleneck in memory design. Traditional Monte Carlo simulations require extensive SPICE calls, which are costly. HOLMES redefines failure-center localization as few-shot classification, combining an SVD-based anisotropic proposal and a hit-rate-driven adaptive mixing scheme to significantly improve efficiency and accuracy. In 6T SRAM benchmarks, HOLMES maintains within 5.9% error across five configurations from D=108 to D=1152, achieving up to 58.8x speedup over Monte Carlo. Despite its strong performance in high-dimensional settings, feature selection and parameter tuning remain challenges for future research.
Deep Analysis
Background
As SRAM arrays scale to smaller process nodes, process variations such as intra-die mismatches, doping fluctuations, and threshold voltage shifts drive circuit performance outside specifications, making yield estimation a critical bottleneck in memory design. Traditional Monte Carlo simulations require extensive SPICE calls, which are costly.
Core Problem
Failure-center localization in high-dimensional settings is challenging, especially with severely imbalanced sample sets. Existing methods rely on iterative gradient-based training, which performs poorly under extreme class imbalance, leading to accuracy collapse in high dimensions.
Innovation
HOLMES redefines failure-center localization as few-shot classification, using TabPFN for gradient-free inference. It combines an SVD-based anisotropic proposal and a hit-rate-driven adaptive mixing scheme, offering a more robust solution.
Methodology
- �� Reformulates failure-center localization as few-shot binary classification.
- �� Uses TabPFN for gradient-free inference, avoiding ill-posed training loops.
- �� Combines SVD-based anisotropic proposal to capture local geometry of failure manifold.
- �� Employs hit-rate-driven adaptive mixing scheme to stabilize importance weights.
Experiments
Experiments are conducted on the OpenYield platform, evaluating SRAM arrays from D=108 to D=1152. Compared against eight importance sampling baselines, including MNIS, HSCS, AIS, etc., using the same initial sampling budgets and SPICE simulation settings.
Results
HOLMES maintains within 5.9% error across five configurations from D=108 to D=1152, achieving up to 58.8x speedup over Monte Carlo. Compared to the strongest baseline, HOLMES achieves 0.1% and 5.9% error at D=864 and D=1152.
Applications
HOLMES can be directly applied to high-sigma yield estimation in SRAM design, significantly reducing computational costs and improving estimation accuracy. Its approach can also be extended to other domains requiring handling of extreme class imbalance.
Limitations & Outlook
Despite its strong performance in high-dimensional settings, feature selection and parameter tuning remain challenges for future research. In certain configurations, hit-rate parameters may need adjustment to ensure stability.
Plain Language Accessible to non-experts
Imagine you are in a giant maze with thousands of rooms, and you need to find the exit. Traditional methods are like checking each room one by one, which is very inefficient. HOLMES is like having a smart guide who can quickly identify which rooms are likely to have an exit, allowing you to focus your efforts on those rooms. This greatly increases the efficiency and accuracy of finding the exit.
ELI14 Explained like you're 14
Imagine you're playing a super complex maze game with thousands of rooms! Traditional methods are like checking each room one by one, super slow. HOLMES is like a smart game assistant who can quickly tell you which rooms might have an exit, so you can focus on those rooms. This way, you can win the game faster!
Glossary
HOLMES (High-sigma Optimal Localization)
A method for high-dimensional yield estimation that locates failure centers through few-shot classification.
Used to solve high-dimensional failure-center localization problems.
TabPFN (Tabular Foundation Model)
A foundation model for tabular data that performs Bayesian classification via in-context learning without gradient updates.
Used in HOLMES for gradient-free inference.
SVD (Singular Value Decomposition)
A linear algebra technique that decomposes a matrix into three matrices, often used for data dimensionality reduction and feature extraction.
Used to capture local geometry of the failure manifold.
Importance Sampling
A statistical technique that estimates expectations by sampling from a specific distribution to improve computational efficiency.
Used to reduce computational costs for high-sigma targets.
Hit Rate
The proportion of failure samples in the proposal distribution during sampling, used to adjust the mixing coefficient.
Used in the adaptive mixing scheme.
Open Questions Unanswered questions from this research
- 1 How to optimize feature selection strategies in extreme high-dimensional settings to improve model generalization.
- 2 Potential and challenges of applying HOLMES to other domains.
Applications
Immediate Applications
SRAM Design
HOLMES can be directly applied to high-sigma yield estimation in SRAM design, significantly reducing computational costs and improving estimation accuracy.
Long-term Vision
Applications in Other Domains
HOLMES's approach can be extended to other domains requiring handling of extreme class imbalance, such as financial risk assessment and medical diagnosis.
Abstract
Importance sampling for high-sigma yield estimation requires locating the failure center from a severely imbalanced sample set. Existing surrogate-assisted methods rely on iterative gradient-based training, ill-posed under extreme class imbalance; model errors propagate into the estimator, causing accuracy collapse in high dimensions. We recast failure-center localization as few-shot binary classification: a prior-fitted tabular foundation model performs gradient-free in-context inference in a single forward pass, eliminating the ill-posed training loop. \textbf{HOLMES} (High-sigma Optimal Localization via Manifold Estimation and Sampling) pairs this with an SVD-based anisotropic proposal that captures the local geometry of the failure manifold, and a hit-rate-driven adaptive mixing scheme that stabilizes importance weights where conventional adaptation collapses. On 6T SRAM benchmarks spanning $D = 108$ to $D = 1{,}152$, full-dimensional baselines exhibit accuracy collapse at some dimension, with the strongest baseline reaching 25.8\% relative error; PCA+MNIS is additionally evaluated at the two largest dimensions. HOLMES remains within 5.9\% across all five configurations with up to $58.8\times$ speedup over Monte Carlo. The code is available on \href{https://github.com/IceLab-JCIE/ICE006-Yield-Holmes}