ULPT: Prompt Tuning with Ultra-Low-Dimensional Optimization

Large language models achieve state-of-the-art performance but are costly to fine-tune due to their size. Parameter-efficient fine-tuning methods, such as prompt tuning, address this by reducing trainable parameters while maintaining strong performance. However, prior methods tie prompt embeddings to the model's dimensionality, which may not scale well with larger LLMs and more customized LLMs. In this paper, we propose Ultra-Low-dimensional Prompt Tuning (ULPT), which optimizes prompts in a low-dimensional space (e.g., 2D) and use a random but frozen matrix for the up-projection. To enhance alignment, we introduce learnable shift and scale embeddings. ULPT drastically reduces the trainable parameters, e.g., 2D only using 2% parameters compared with vanilla prompt tuning while retaining most of the performance across 21 NLP tasks. Our theoretical analysis shows that random projections can capture high-rank structures effectively, and experimental results demonstrate ULPT's competitive performance over existing parameter-efficient methods.