# Stabilizing Black-Box Prompt Optimization with Textual Regularization and Signal Aggregation

arXiv: https://arxiv.org/abs/2507.09839 · HTML: https://mlsanity.com/paper/2507.09839/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 64 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 30 of 50)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)

## Built on by (most cited first, 2 of 2)

- [UniAPO: Unified Multimodal Automated Prompt Optimization](https://mlsanity.com/paper/2508.17890/) (2025)
- [Joint Workflow and Prompt Optimization for User Behavior Simulation](https://mlsanity.com/paper/2610.07663/) (2026)

## Abstract (arXiv)

An increasing number of NLP applications interact with large language models (LLMs) through black-box APIs, making prompt engineering critical for controlling model behavior. Recent Automatic Prompt Optimization (APO) methods iteratively refine prompts using model-generated critiques (often called textual gradients), but they predominantly optimize from failures and underutilize information contained in correct predictions, leading to instability and semantic drift. We propose TRAS (Textual Regularization with Aggregated Signals), a feedback-centric framework that is plug-and-play with existing APO search backbones. It retains the standard textual gradient signal from prior work for error correction and introduces a complementary textual regularizer derived from successful predictions to preserve beneficial prompt components. Because both signals are stochastic and can be noisy, we further introduce Monte Carlo Signal Aggregation (MCSA), which samples multiple gradients or regularizers and aggregates them into a single actionable directive, emphasizing consistent, actionable advice while filtering out outliers. Motivated by rapid model churn, we also formalize Automatic Prompt Migration (APM), the practical problem of adapting an expert prompt across model versions or API providers without losing critical instructions. Across standard APO and APM scenarios, our approach consistently outperforms strong baselines, yielding higher accuracy, faster convergence, and lower query cost, while substantially reducing the degradation observed under naive prompt migration.