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This paper investigates the efficiency of prompt learning in vision-language models by factorizing the dense prompt matrix used in Context Optimization (CoOp) into two components, significantly reducing the number of trainable parameters. The authors demonstrate that low-rank prompts can achieve comparable or superior performance to traditional dense prompts across various few-shot benchmarks while requiring fewer parameters, particularly excelling in low-shot generalization scenarios. Notably, fixing the token-side factor of the prompt matrix to various bases (e.g., Gaussian or random) does not hinder performance, emphasizing the adaptability of the embedding-side factor for effective model training.
Low-rank prompt learning can match or exceed the performance of dense prompts while slashing trainable parameters, revealing that a fixed token basis suffices for effective adaptation.
Prompt learning adapts CLIP to downstream recognition by replacing hand-written templates with learned continuous context vectors, which in Context Optimization (CoOp) form a dense prompt matrix $\mathbf{P}\in\mathbb{R}^{m\times d}$ trained from only a few examples per class. We study whether this matrix is over-parameterized by factorizing it as $\mathbf{P}=\mathbf{B}\mathbf{A}$, which cuts the trainable prompt parameters from $md$ to $r(m+d)$, and to $rd$ once the token-side factor $\mathbf{B}$ is fixed. Across seven few-shot benchmarks and two CLIP backbones, low-rank prompts match or improve dense CoOp at far fewer parameters, with the clearest gains on low-shot base-to-new generalization. We then find that the token-side factor need not be learned at all: fixing $\mathbf{B}$ to a Gaussian, orthogonal, SVD-derived, or even random basis and training only the embedding-side factor $\mathbf{A}$ stays on par with the fully trainable factorization, and a source-trained $\mathbf{B}$ offers no advantage over a random one. A prompt-factor asymmetry and a local update-space dimension gap show why fixing $\mathbf{B}$ is far less restrictive than fixing $\mathbf{A}$, and a smoothness-only guarantee certifies that optimizing $\mathbf{A}$ over a fixed $\mathbf{B}$ converges. In the CLIP prompt setting, the embedding-side coefficients carry the adaptation while the token basis can simply be fixed.
