cs.CVSep 8, 2026

Low-Rank Prompt Learning for Vision-Language Models with Fixed-Token Bases

Authors: Tanvir Muntakim TonoySajjad GhiasvandMahnoosh AlizadehRamtin Pedarsani

Abstract

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 PRm×d\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 P=BA\mathbf{P}=\mathbf{B}\mathbf{A}, which cuts the trainable prompt parameters from mdmd to r(m+d)r(m+d), and to rdrd once the token-side factor B\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 B\mathbf{B} to a Gaussian, orthogonal, SVD-derived, or even random basis and training only the embedding-side factor A\mathbf{A} stays on par with the fully trainable factorization, and a source-trained B\mathbf{B} offers no advantage over a random one. A prompt-factor asymmetry and a local update-space dimension gap show why fixing B\mathbf{B} is far less restrictive than fixing A\mathbf{A}, and a smoothness-only guarantee certifies that optimizing A\mathbf{A} over a fixed B\mathbf{B} converges. In the CLIP prompt setting, the embedding-side coefficients carry the adaptation while the token basis can simply be fixed.

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