Eliciting Fine-Tuned Transformer Capabilities via Inference-Time Techniques

Large language models have transformed natural language processing, yet supervised fine-tuning (SFT) remains computationally intensive. This paper formally proves that capabilities acquired through SFT can be approximated by a base transformer model using inference-time techniques, specifically in-context learning (ICL), without altering model parameters, under idealized assumptions including unbounded computational resources and access to the fine-tuning dataset. We extend these results to practical scenarios with finite context lengths and partial dataset access. For text generation tasks with fixed output length $l$, datasets of size $\mathrm{O}\left( \frac{m V}{\varepsilon^2} \log \frac{m}{\delta} \right)$ or, with bounded context, $\mathrm{O}\left( \frac{l \log V}{\varepsilon^2} \log \frac{1}{\delta} \right)$ suffice to approximate fine-tuned behavior across $m$ contexts within error $\varepsilon$, where $V$ is the vocabulary size and $\delta$ is the failure probability. For linear classification, datasets of size $\mathrm{O}\left( \frac{d}{\varepsilon} \right)$ or, with fixed context, $\mathrm{O}\left( \frac{1}{\varepsilon^2} \log \frac{1}{\delta} \right)$ are sufficient, where $d$ is the input dimension. Grounded in the Turing completeness of transformers, these results provide a theoretical foundation for resource-efficient deployment of large language models, with practical techniques like retrieval-augmented generation bridging theory to real-world applications.