Few-Shot Test-Time Optimization Without Retraining for Semiconductor Recipe Generation and Beyond

TL;DR

The paper tackles the challenge of adapting deployed models or hardware without retraining. It introduces Model Feedback Learning (MFL), a two-loop input-optimization framework that uses a fixed emulator $\mathcal{E}$ and a learnable reverse emulator $\mathcal{R}$ to map targets $Z'$ to inputs $X'$ for a fixed model $\mathcal{M}$, with Loop A aligning $\mathcal{R}$ to $\mathcal{E}$ and Loop B refining toward $\mathcal{M}$. A conservative learning strategy based on model sensitivities $s_{\mathcal{E}}(x)$ and $s_{\mathcal{M}}(x)$ stabilizes updates, and domain randomization improves robustness. Empirically, MFL achieves target semiconductor plasma-etching recipes in as few as five iterations, outperforming Bayesian optimization and human experts, and it generalizes to chemical vapor deposition and wire bonding while maintaining robustness to process variability. The work demonstrates that retraining-free input optimization can be both data-efficient and broadly applicable to real-world manufacturing and control tasks.

Abstract

We introduce Model Feedback Learning (MFL), a novel test-time optimization framework for optimizing inputs to pre-trained AI models or deployed hardware systems without requiring any retraining of the models or modifications to the hardware. In contrast to existing methods that rely on adjusting model parameters, MFL leverages a lightweight reverse model to iteratively search for optimal inputs, enabling efficient adaptation to new objectives under deployment constraints. This framework is particularly advantageous in real-world settings, such as semiconductor manufacturing recipe generation, where modifying deployed systems is often infeasible or cost-prohibitive. We validate MFL on semiconductor plasma etching tasks, where it achieves target recipe generation in just five iterations, significantly outperforming both Bayesian optimization and human experts. Beyond semiconductor applications, MFL also demonstrates strong performance in chemical processes (e.g., chemical vapor deposition) and electronic systems (e.g., wire bonding), highlighting its broad applicability. Additionally, MFL incorporates stability-aware optimization, enhancing robustness to process variations and surpassing conventional supervised learning and random search methods in high-dimensional control settings. By enabling few-shot adaptation, MFL provides a scalable and efficient paradigm for deploying intelligent control in real-world environments.

Figures (10)

• Figure 1: Schematic of the semiconductor manufacturing process, showing the incoming photoresist mask, recipe inputs (e.g., gas flows, plasma powers, pulsing parameters, and wafer temperature), and the resulting etched profiles kanarik2023human. The emulator/machine outputs include etch depth, etch rate, mask remaining, top CD, $\Delta$CD, and bow CD. Deviations (as seen in the mismatch between target and actual profiles) can occur due to process variability.
• Figure 2: Illustration of standard supervised learning.
• Figure 3: Two-loop training process for the reverse emulator model $\mathcal{R}$: Pre-train $\mathcal{R}$ using an emulator model $\mathcal{E}$ in Loop A and tune $\mathcal{R}$ using the machine model $\mathcal{M}$ in Loop B.
• Figure 4: Illustration for the approximation errors of the emulator $\mathcal{E}$. For a given target $Y_i$, $X_i$ denotes the corresponding machine input, and $\widehat{X}_i$ denotes the emulator input.
• Figure 5: Comparison of MFL and supervised learning in high-dimensional space training, conducted across three random seeds. The y-axis refers to the output error per epoch in a six-dimensional target space.

Theorems & Definitions (5)

• Definition 1: Model sensitivity
• Remark 1: Convergence of Algorithm \ref{['alg:algorithm-mfl']}
• Remark 2: Broader application of MFL
• Theorem B.1
• proof : Proof of Theorem \ref{['thm: convergence']}