# Understanding prompt engineering may not require rethinking generalization

arXiv: https://arxiv.org/abs/2310.03957 · HTML: https://mlsanity.com/paper/2310.03957/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 42 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [Prompt learning and adaptation of CLIP](https://mlsanity.com/mllm/prompt-learning-and-adaptation-of-clip/)

## Builds on (most cited first, 30 of 32)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Making Pre-trained Language Models Better Few-shot Learners](https://mlsanity.com/paper/2012.15723/) (2020)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Hard Prompts Made Easy: Gradient-Based Discrete Optimization for Prompt Tuning and Discovery](https://mlsanity.com/paper/2302.03668/) (2023)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [PromptSource: An Integrated Development Environment and Repository for Natural Language Prompts](https://mlsanity.com/paper/2202.01279/) (2022)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [How Many Data Points is a Prompt Worth?](https://mlsanity.com/paper/2103.08493/) (2021)
- [ZeroCap: Zero-Shot Image-to-Text Generation for Visual-Semantic Arithmetic](https://mlsanity.com/paper/2111.14447/) (2021)
- [Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach](https://mlsanity.com/paper/1804.05862/) (2018)
- [In Search of Robust Measures of Generalization](https://mlsanity.com/paper/2010.11924/) (2020)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)

## Built on by (most cited first, 10 of 10)

- [Unlocking Tokens as Data Points for Generalization Bounds on Larger Language Models](https://mlsanity.com/paper/2407.18158/) (2024)
- [Automated Black-box Prompt Engineering for Personalized Text-to-Image Generation](https://mlsanity.com/paper/2403.19103/) (2024)
- [Predicting the Performance of Black-box LLMs through Follow-up Queries](https://mlsanity.com/paper/2501.01558/) (2025)
- [Finetuning CLIP to Reason about Pairwise Differences](https://mlsanity.com/paper/2409.09721/) (2024)
- [Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers](https://mlsanity.com/paper/2509.22445/) (2025)
- [Compute-Optimal LLMs Provably Generalize Better With Scale](https://mlsanity.com/paper/2504.15208/) (2025)
- [Prompts Generalize with Low Data: Non-vacuous Generalization Bounds for Optimizing Prompts with More Informative Priors](https://mlsanity.com/paper/2510.08413/) (2025)
- [What Fits (Into Few Tokens) Doesn't Overfit: Compression and Generalization in ML Research Agents](https://mlsanity.com/paper/2606.11045/) (2026)
- [Non-vacuous Generalization Bounds for Deep Neural Networks without any modification to the trained models](https://mlsanity.com/paper/2503.07325/) (2025)
- [Aligning Probabilistic Beliefs under Informative Missingness: LLM Steerability in Clinical Reasoning](https://mlsanity.com/paper/2512.00479/) (2025)

## Abstract (arXiv)

Zero-shot learning in prompted vision-language models, the practice of crafting prompts to build classifiers without an explicit training process, has achieved impressive performance in many settings. This success presents a seemingly surprising observation: these methods suffer relatively little from overfitting, i.e., when a prompt is manually engineered to achieve low error on a given training set (thus rendering the method no longer actually zero-shot), the approach still performs well on held-out test data. In this paper, we show that we can explain such performance well via recourse to classical PAC-Bayes bounds. Specifically, we show that the discrete nature of prompts, combined with a PAC-Bayes prior given by a language model, results in generalization bounds that are remarkably tight by the standards of the literature: for instance, the generalization bound of an ImageNet classifier is often within a few percentage points of the true test error. We demonstrate empirically that this holds for existing handcrafted prompts and prompts generated through simple greedy search. Furthermore, the resulting bound is well-suited for model selection: the models with the best bound typically also have the best test performance. This work thus provides a possible justification for the widespread practice of prompt engineering, even if it seems that such methods could potentially overfit the training data.