HOLMES: In-Context Failure-Center Localization for High-Dimensional Yield Estimation

Wei W. Xing; Xixi Zhou; Kaiqi Huang; Jiaye Pan; Hong Qiu; Xin Wang; Shan Shen

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HOLMES: In-Context Failure-Center Localization for High-Dimensional Yield Estimation

Wei W. Xing, Xixi Zhou, Kaiqi Huang, Jiaye Pan, Hong Qiu, Xin Wang, Shan Shen

arXiv:2608.26758v1Aug 27, 2026cs.AR

TL;DR

High-sigma SRAM yield estimation must locate a failure center from severely imbalanced samples, but fitting parametric models is ill-posed. HOLMES reformulates localization as few-shot classification with gradient-free in-context inference, combines it with anisotropic proposals and hit-rate adaptation, and remains within 5.9% relative error across five benchmark configurations.

Problem
Failure-center localization for importance sampling must infer failure-region candidates from a severely imbalanced labeled dataset containing few failures and thousands of non-failures.
Method
HOLMES uses a prior-fitted tabular foundation model for single-pass gradient-free in-context classification, an SVD-based anisotropic proposal, and hit-rate-driven adaptive mixing.
Results
HOLMES remains within 5.9% relative error across all five 6T SRAM configurations, while full-dimensional baselines collapse at some dimension and the strongest baseline reaches 25.8% error.
Takeaways & Limitations
Recasting failure-center localization as few-shot classification eliminates the ill-posed training loop without sacrificing localization accuracy.
Takeaways & Limitations
The current formulation assumes a single dominant failure region.

Abstract

from arXiv · show

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}

1 Introduction

High-dimensional SRAM yield estimation makes failure-center localization difficult because failures are rare, while existing fitting and adaptation strategies can become unstable. HOLMES reformulates localization as few-shot classification and combines in-context inference with geometry-aware proposals and hit-rate adaptation.

Motivation: SRAM variation grows from D = 108 in a 3×2 array to D = 1,152 in an 8×8 array, making failure-region localization increasingly difficult.Monte Carlo requires O(1/P_f) SPICE calls, demanding 10^7 or more evaluations for high-sigma targets.
Limitations of existing methods: Existing surrogate-assisted methods use iterative gradient-based training that is ill-posed under extreme class imbalance, allowing model errors to propagate into the importance-sampling estimator.Analytic alternatives avoid gradient training but impose strong distributional assumptions.
Reformulation: HOLMES recasts failure-center localization as few-shot binary classification, enabling gradient-free in-context inference by a prior-fitted tabular foundation model in one forward pass.The reformulation eliminates the ill-posed training loop while targeting the decision boundary between fail and pass regions.
HOLMES design: HOLMES constructs a failure-preserving context set, uses SVD for an anisotropic proposal aligned with the failure manifold, and adapts proposal mixing through the hit rate.The workflow ranks candidates using normalized prior and failure-probability terms, then centers the proposal on the top-scoring samples.
Evaluation: 5.9% relative error is the maximum reported for HOLMES across five 6T SRAM configurations spanning D = 108 to D = 1,152, while the strongest baseline reaches 25.8%.PCA+MNIS is additionally evaluated at D = 864 and D = 1,152.

2 Preliminaries

The preliminaries define high-sigma yield estimation as estimating failure probability under expensive SPICE evaluation and motivate importance sampling through the failure center. They frame center localization as few-shot classification and present TabPFN as a gradient-free, in-context solution.

Problem definition: The process-variation vector x ∈ R^D is modeled with independent standard-Gaussian parameters, and SPICE evaluates circuit performance for each sampled x.A design fails when performance violates a predefined specification.
Problem definition: The goal is to estimate P_f accurately with as few SPICE calls as possible.
Monte Carlo: Monte Carlo needs approximately N ≈ 100/P_f samples for 90% accuracy with 90% confidence, leading to 10^7 or more SPICE evaluations for high-sigma targets.
Importance sampling: Importance sampling draws from a proposal q(x) and reweights samples, with variance minimized by an optimal proposal concentrated over the failure region according to prior density.
Failure center: The failure center is the highest-prior-probability point in the failure region and reduces to the minimum-norm failure point under a standard-Gaussian prior.Centering the proposal nearer x* reduces estimator variance by reducing samples wasted outside the failure region.
Failure center: Because each iteration may contain only a few failures among thousands of non-failures, locating x* is a few-shot binary classification problem.
TabPFN: TabPFN performs Bayesian in-context classification from a labeled context set and outputs posterior failure probabilities for query points in a single forward pass without gradient updates.Its prior is learned from synthetic datasets and supports inference without retraining between iterations.

3 Proposed Method

HOLMES localizes the failure center through gradient-free, in-context classification, then constructs an anisotropic importance-sampling proposal and adapts exploration using failure hit rates.

In-Context Failure-Center Localization: HOLMES scores observed failures and proposal candidates by combining normalized log-prior density with predicted failure probability.Soft predictions extend ranking beyond observed failures, while separate z-normalization prevents either component from dominating.
In-Context Failure-Center Localization: TabPFN performs approximate Bayesian inference from the context in one transformer forward pass without gradients or retraining between iterations.This supports classification from only a few failure instances per iteration under extreme imbalance.
In-Context Failure-Center Localization: Failure-preserving context construction allocates the context budget to failures first and fills remaining capacity with boundary-representative non-failures.This prevents random context subsampling from omitting the rare failure class.
SVD-Based Anisotropic Proposal Construction: The top-m high-score samples define the empirical proposal center, which is used to center the neighborhood before SVD estimates its principal directions and variation scales.The resulting covariance stretches sampling along retained failure-manifold directions.
High-Dimensional Feature Selection: When D exceeds TabPFN’s input limit, importance-weighted mutual information selects the K features most informative under the prior distribution.Resampling corrects proposal-induced bias before mutual-information estimation and TabPFN inference.
SVD-Based Anisotropic Proposal Construction: As dimension grows, the failure manifold occupies a thinner subspace, making anisotropic sampling increasingly distinct from isotropic sampling.An isotropic Gaussian wastes samples in directions orthogonal to the manifold.
Hit-Rate-Driven Adaptive Mixing: The mixture distribution combines the prior and learned proposal, with its coefficient adapted from hit rate rather than ESS to preserve exploration when proposal effectiveness changes.The coefficient increases above the target hit rate, decreases below it, and is held constant when too few proposal samples make the estimate unreliable.
Adaptive Importance Sampling: HOLMES initializes with prior sampling, iteratively updates its proposal, and terminates after the failure-rate estimate’s coefficient of variation falls below the specified threshold and minimum iterations are met.The complete workflow is summarized in Algorithm 1.

4 Experimental Results

Experiments evaluate HOLMES on OpenYield SRAM arrays across dimensions from 108 to 1,152, comparing runtime, robustness, yield-estimation error, classifier choice, and component ablations. HOLMES remains accurate across dimensions while baselines and individual component removals show dimension-dependent failures.

Experimental Setup: Experiments use OpenYield macro-level SRAM designs with read delay as the primary performance metric and MC as the reference estimator.Arrays span D = 108, 576, 756, 864, and 1,152 under identical evaluation conditions.
Computational Overhead: At D = 576, model computation takes 637.1 seconds, or 2.3% of HOLMES’s runtime, yielding a 19.3× wall-clock speedup.The wall-clock speedup closely matches the 19.8× simulation-count speedup, so TabPFN inference does not offset saved SPICE evaluations.
Statistical Robustness: Across five independent runs with fixed τ = 0.1, mean relative errors are 3.3%, 1.8%, and 0.7% at D = 108, 576, and 864, with CV at most 3.6%.These results indicate stable estimates on the three tested configurations without dimension-specific scheduling.
Main Results: HOLMES remains within 5.9% error across all dimensions, whereas every full-dimensional baseline collapses at some dimension with peak errors of 24.5–100%.PCA+MNIS records 5.67% and 12.50% error at D = 864 and D = 1,152, versus 0.1% and 5.9% for HOLMES.
Classifier Substitution: At D = 864, replacing TabPFN with conventional classifiers produces 28.7–73.8% error, compared with 0.1% for TabPFN under identical sampling components.The comparison isolates failure-center localization as the decisive differing factor in this experiment.
Ablation Study: Removing the anisotropic proposal raises relative error to 14.53%, 20.36%, and 11.88% at D = 108, 576, and 864, while removing adaptive mixing reaches 40.95% at D = 108.The ablations identify SVD alignment and hit-rate adaptation as complementary safeguards for proposal quality and exploration.

5 Conclusion

HOLMES reframes failure-center localization as few-shot binary classification, enabling gradient-free in-context inference without the ill-posed training loop. Combined with anisotropic proposals and adaptive mixing, it remains accurate across high-dimensional 6T SRAM benchmarks where baselines collapse.

HOLMES reframes failure-center localization as few-shot binary classification and uses a prior-fitted tabular foundation model for gradient-free in-context inference.This eliminates the ill-posed iterative training loop while preserving localization accuracy.
HOLMES combines the reformulation with an SVD-based anisotropic proposal and a hit-rate-driven adaptive mixing scheme.The ablation study reports that removing either component substantially increases error in tested configurations.
5.9% relative error is the maximum reported across all five 6T SRAM configurations spanning D = 108 to D = 1,152.Full-dimensional baselines collapse at some dimension, with the strongest baseline reaching 25.8% error.
A single dominant failure region is assumed, leaving multicenter localization for well-separated failure modes as future work.