# Forward and Inverse Virtual Metrology for Phototransistor Gain: A Hierarchical, Uncertainty-Aware Approach for Small Production Datasets

arXiv: https://arxiv.org/abs/2608.11868 · HTML: https://mlsanity.com/paper/2608.11868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [A Survey of Data Quality Measurement and Monitoring Tools](https://mlsanity.com/paper/1907.08138/) (2019)
- [The Effects of Data Quality on Machine Learning Performance on Tabular Data](https://mlsanity.com/paper/2207.14529/) (2022)
- [A Survey on Data Quality Dimensions and Tools for Machine Learning](https://mlsanity.com/paper/2406.19614/) (2024)
- [End-to-End Data Quality-Driven Framework for Machine Learning in Production Environment](https://mlsanity.com/paper/2512.19723/) (2025)

## Abstract (arXiv)

The customization, optimization and stabilization of the process flow of a silicon bipolar phototransistor commits months of cleanroom time before a finished device can be measured, so a model that predicts device gain from process parameters before a run has value out of proportion to its accuracy. We study this problem on a real fabrication history, thirteen to fourteen process runs of a single device: a small-sample, hierarchically structured setting unlike the large-corpus regime of conventional virtual metrology. Decomposing the variance of device gain, we find that roughly half of it lies between process runs rather than within them, so recipe-only prediction is bounded by construction. Building on these findings we provide a forward gain predictor with a relative, uncertainty-aware signal, an inverse search that returns recipes for a target gain, and, as the foundation for all of it, a multi-level data-quality assessment tailored to the nested physical entities of fabrication (batch, wafer, die) with an explicit cross-level linkage score. The normalized dataset and analysis code are released for full reproducibility.