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This paper provides a rigorous theoretical proof establishing the conditions under which prefix-tuning can generate arbitrary output sequences in pretrained Transformers, resolving an open question regarding the method's expressiveness. By demonstrating that a valid prefix exists if and only if the target output is within the model's range, the authors offer a constructive algorithm verified on GPT-2 and Qwen models to achieve precise control over generation.
Prefix-Tuning for Arbitrary Output Sequences on Pretrained Transformers
arXiv:2610.24123v1 Announce Type: cross Abstract: Prefix-tuning is a parameter-efficient fine-tuning method for large language models (LLMs) that steers model outputs by prepending task-specific prefix representations to the input sequence. Despite its practical success, the theoretical understanding of the expressiveness of prefixes remains incomplete. In particular, the following question remains open: Given a pretrained autoregressive Transformer, for any input-output sequence pair $(\mathtt{x},\mathtt{y})$, does there always exist a prefix $\mathcal{S}$ such that prepending $\mathcal{S}$ to $\mathtt{x}$ induces the model to generate the target output $\mathtt{y}$? In this work, we prove that under the assumption that $\mathtt{y}$ is in the range of the pretrained Transformer, such a prefix $\mathcal{S}$ exists and can be explicitly computed by solving multiple linear systems. We further show that this assumption is necessary, in the sense that such a prefix may not exist when the assumption fails, thereby providing a complete answer to the above question. Our analysis is constructive and the obtained theoretical results hold under fairly general assumptions on model architecture. Extensive experiments on GPT-2 and Qwen3-4B demonstrate that our algorithm produces prefixes with strong control over model outputs.
Abstract:Prefix-tuning is a parameter-efficient fine-tuning method for large language models (LLMs) that steers model outputs by prepending task-specific prefix representations to the input sequence. Despite its practical success, the theoretical understanding of the expressiveness of prefixes remains incomplete. In particular, the following question remains open: Given a pretrained autoregressive Transformer, for any input-output sequence pair $(\mathtt{x},\mathtt{y})$, does there always exist a prefix $\mathcal{S}$ such that prepending $\mathcal{S}$ to $\mathtt{x}$ induces the model to generate the target output $\mathtt{y}$? In this work, we prove that under the assumption that $\mathtt{y}$ is in the range of the pretrained Transformer, such a prefix $\mathcal{S}$ exists and can be explicitly computed by solving multiple linear systems. We further show that this assumption is necessary, in the sense that such a prefix may not exist when the assumption fails, thereby providing a complete answer to the above question. Our analysis is constructive and the obtained theoretical results hold under fairly general assumptions on model architecture. Extensive experiments on GPT-2 and Qwen3-4B demonstrate that our algorithm produces prefixes with strong control over model outputs.
Accepted at NeurIPS 2026. Code: this https URL. Online demo: this https URL
Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2610.24123 [cs.CL]
(or arXiv:2610.24123v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2610.24123 Focus to learn more arXiv-issued DOI via DataCite
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