# When Do Prompting and Prefix-Tuning Work? A Theory of Capabilities and Limitations

arXiv: https://arxiv.org/abs/2310.19698 · HTML: https://mlsanity.com/paper/2310.19698/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 57 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [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)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Recent Advances in Natural Language Processing via Large Pre-Trained Language Models: A Survey](https://mlsanity.com/paper/2111.01243/) (2021)
- [Learning How to Ask: Querying LMs with Mixtures of Soft Prompts](https://mlsanity.com/paper/2104.06599/) (2021)
- [Black-Box Tuning for Language-Model-as-a-Service](https://mlsanity.com/paper/2201.03514/) (2022)
- [SPoT: Better Frozen Model Adaptation through Soft Prompt Transfer](https://mlsanity.com/paper/2110.07904/) (2021)
- [WARP: Word-level Adversarial ReProgramming](https://mlsanity.com/paper/2101.00121/) (2021)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)
- [DART: Open-Domain Structured Data Record to Text Generation](https://mlsanity.com/paper/2007.02871/) (2020)
- [The Learnability of In-Context Learning](https://mlsanity.com/paper/2303.07895/) (2023)

## Built on by (most cited first, 30 of 43)

- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Retrieval Augmented Generation (RAG) and Beyond: A Comprehensive Survey on How to Make your LLMs use External Data More Wisely](https://mlsanity.com/paper/2409.14924/) (2024)
- [Combining Fine-Tuning and LLM-based Agents for Intuitive Smart Contract Auditing with Justifications](https://mlsanity.com/paper/2403.16073/) (2024)
- [R2-Tuning: Efficient Image-to-Video Transfer Learning for Video Temporal Grounding](https://mlsanity.com/paper/2404.00801/) (2024)
- [How Much Can RAG Help the Reasoning of LLM?](https://mlsanity.com/paper/2410.02338/) (2024)
- [Code Simulation Challenges for Large Language Models](https://mlsanity.com/paper/2401.09074/) (2024)
- [Revisiting Prefix-tuning: Statistical Benefits of Reparameterization among Prompts](https://mlsanity.com/paper/2410.02200/) (2024)
- [Parameter-Efficient Fine-Tuning of State Space Models](https://mlsanity.com/paper/2410.09016/) (2024)
- [Re-Imagining Multimodal Instruction Tuning: A Representation View](https://mlsanity.com/paper/2503.00723/) (2025)
- [Prompt Tuning Strikes Back: Customizing Foundation Models with Low-Rank Prompt Adaptation](https://mlsanity.com/paper/2405.15282/) (2024)
- [GeLoRA: Geometric Adaptive Ranks For Efficient LoRA Fine-tuning](https://mlsanity.com/paper/2412.09250/) (2024)
- [Towards Incremental Learning in Large Language Models: A Critical Review](https://mlsanity.com/paper/2404.18311/) (2024)
- [PromptExp: Multi-granularity Prompt Explanation of Large Language Models](https://mlsanity.com/paper/2410.13073/) (2024)
- [Understanding Prompt Tuning and In-Context Learning via Meta-Learning](https://mlsanity.com/paper/2505.17010/) (2025)
- [Domain Adaptation of LLMs for Process Data](https://mlsanity.com/paper/2509.03161/) (2025)
- [MoPE: Mixture of Prompt Experts for Parameter-Efficient and Scalable Multimodal Fusion](https://mlsanity.com/paper/2403.10568/) (2024)
- [Revisit Visual Prompt Tuning: The Expressiveness of Prompt Experts](https://mlsanity.com/paper/2501.18936/) (2025)
- ["Let's Argue Both Sides": Argument Generation Can Force Small Models to Utilize Previously Inaccessible Reasoning Capabilities](https://mlsanity.com/paper/2410.12997/) (2024)
- [Why is prompting hard? Understanding prompts on binary sequence predictors](https://mlsanity.com/paper/2502.10760/) (2025)
- [Efficient Knowledge Transfer in Multi-Task Learning through Task-Adaptive Low-Rank Representation](https://mlsanity.com/paper/2505.00009/) (2025)
- [Neural Network Reprogrammability: A Unified Theme on Model Reprogramming, Prompt Tuning, and Prompt Instruction](https://mlsanity.com/paper/2506.04650/) (2025)
- [PrefixMemory-Tuning: Modernizing Prefix-Tuning by Decoupling the Prefix from Attention](https://mlsanity.com/paper/2506.13674/) (2025)
- [Memory Limitations of Prompt Tuning in Transformers](https://mlsanity.com/paper/2509.00421/) (2025)
- [EmoCtrl: Controllable Emotional Image Content Generation](https://mlsanity.com/paper/2512.22437/) (2025)
- [Skill Neologisms: Towards Skill-based Continual Learning](https://mlsanity.com/paper/2605.04970/) (2026)
- [SoftSRV: Learn to Generate Targeted Synthetic Data](https://mlsanity.com/paper/2410.16534/) (2024)
- [ADePT: Adaptive Decomposed Prompt Tuning for Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2501.03291/) (2025)
- [ReasonCACHE: Teaching LLMs To Reason Without Weight Updates](https://mlsanity.com/paper/2602.02366/) (2026)
- [From Noise to Diversity: Random Embedding Injection in LLM Reasoning](https://mlsanity.com/paper/2605.11936/) (2026)
- [Learned Structure in Cartridges: Keys as Shareable Routers in Self-Studied Representations](https://mlsanity.com/paper/2508.17032/) (2025)

## Abstract (arXiv)

Context-based fine-tuning methods, including prompting, in-context learning, soft prompting (also known as prompt tuning), and prefix-tuning, have gained popularity due to their ability to often match the performance of full fine-tuning with a fraction of the parameters. Despite their empirical successes, there is little theoretical understanding of how these techniques influence the internal computation of the model and their expressiveness limitations. We show that despite the continuous embedding space being more expressive than the discrete token space, soft-prompting and prefix-tuning are potentially less expressive than full fine-tuning, even with the same number of learnable parameters. Concretely, context-based fine-tuning cannot change the relative attention pattern over the content and can only bias the outputs of an attention layer in a fixed direction. This suggests that while techniques like prompting, in-context learning, soft prompting, and prefix-tuning can effectively elicit skills present in the pretrained model, they may not be able to learn novel tasks that require new attention patterns.