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When Do Prompting and Prefix-Tuning Work? A Theory of Capabilities and Limitations
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Theoretically and empirically shows that prefix-tuning and soft prompting are more expressive than prompting but cannot change relative attention patterns, so they can elicit or combine pretrained skills but not learn entirely new attention-dependent tasks.
Problem
Lack of theoretical understanding of how context-based fine-tuning methods (prompting, in-context learning, soft prompting, prefix-tuning) change a transformer's internal computation and what their expressiveness limits are compared with full fine-tuning.
Approach
Formalizes prompting, soft prompting and prefix-tuning in a transformer framework and proves that a prefix only rescales attention over content tokens and adds a constant-direction bias to attention outputs, so it cannot change attention patterns; supports this with constructions and small-transformer experiments.
Key results
- Prefix-tuning a model pretrained on ascending sort to sort descending reaches 0% accuracy, while full fine-tuning reaches 85%.
- Prefix-tuning elicits pretrained skills with >90% accuracy on each of four tasks in a 1-layer, 4-head model.
- A rank-1 LoRA on MLPs reaches 92% on the double histogram task, while a prefix of size 12 with the same parameter count reaches 0%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Tune a prefix of size 1 on descending sorting instead of full fine-tuning | Transformer pretrained on ascending sorting · Sorting descending | accuracy: 85$\pm$5% -> 0$\pm$0% | Hurt |
| Tune a prefix of size 1 to elicit a task already present in pretraining | 1-layer, 4-head transformer pretrained on ascending, descending, +1, and +2 · Ascending, descending, +1, and +2 tasks | accuracy: 25$\pm$13% -> 95$\pm$ 2%; 25$\pm$12% -> 90$\pm$ 3%; 24$\pm$11% -> 95$\pm$ 6%; 22$\pm$7% -> 98$\pm$5% | Helped |
| Tune a prefix of size 12 to combine ascending sorting and +1 skills | 40-layer, 4-head transformer pretrained on four tasks · Novel ascending-sort then +1 task | accuracy: 0% -> 93% | Helped |
| Tune a prefix of size 12 on a task requiring new skills | 40-layer, 4-head transformer pretrained on four tasks · Double histogram task | accuracy: 0% -> 1% | No clear effect |
| Use rank-1 LoRA on MLPs instead of a same-parameter-count prefix | 4-layer, 4-head transformer pretrained on four tasks · Double histogram task | accuracy: 0% -> 92% | Helped |
Surprising findings
- Prefix-tuning can fail to learn a new task (descending sort) that full fine-tuning learns easily, despite prefix-tuning being more expressive than prompting in principle.
- In LLaMA and GPT-2 the attention over prefix positions is nearly constant across inputs, so the effective bias subspace collapses.
Limitations
- Analysis is largely limited to toy problems and small transformers rather than large-scale pretrained models.
- Theory covers prefixing and suffix-tuning; suffixing with prompts or soft prompts is not covered.
- Universal approximation and parameter-efficiency conditions are left as open questions.
Experimental setup
Datasets: DART Emotion
Benchmarks: sorting (ascending/descending) add-one and add-two toy tasks double histogram task
Metrics: accuracy attention distribution
Baselines: full fine-tuning LoRA
Builds on: prefix-tuning prompt tuning LoRA Transformer
Closest papers by meaning
- Understanding Prompt Tuning and In-Context Learning via Meta-Learning (NeurIPS 2025 · similarity 0.91)
- Revisiting Prefix-tuning: Statistical Benefits of Reparameterization among Prompts (ICLR 2025 · similarity 0.90)
- Understanding Catastrophic Forgetting in Language Models via Implicit Inference (ICLR 2024 · similarity 0.88)
- Revisiting the Power of Prompt for Visual Tuning (ICML 2024 · similarity 0.88)
- On the Loss of Context Awareness in General Instruction Fine-tuning (NeurIPS 2025 · similarity 0.87)
- Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks (ICLR 2024 · similarity 0.87)
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