The Blending Ratio Is Not Where the Performance Is: Diagnosing Prototype Blending for Few-Shot Adaptation of Vision-Language Models

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arXiv:2608.23634v1 Announce Type: cross Abstract: Many few-shot adaptation methods for vision-language models classify with a convex combination of the zero-shot text prototype and the mean of the K labelled image features, with a single blending ratio routinely tuned on held-out labels, often on the test set itself. We ask what the family's own bias-variance justification invites: what is the right ratio, can it be estimated without validation data, and is finding it where the performance is? First, the ratio minimising prototype mean-squared error has a closed form whose support-set plug-in is exactly a positive-part James-Stein coefficient shrinking towards the text prototype. Across 4,800 cells (ten datasets, five backbones including SigLIP, five shot counts, five seeds, four prompt tiers) this theoretically optimal ratio is a reliable estimate of the wrong quantity: on the 950 primary-tier cells where it is defined it trails a test-set-oracle ratio by 8.5 points. It saturates near 1, discarding the text prior for a nearest-class-mean classifier, because 78% of the text-image prototype distance it treats as bias is a class-independent offset that the arg max largely cancels. We prove the mechanism and bound its share of the damage at 26% by a counterfactual. Second, leave-one-out on the support set alone sets a ratio landing within 0.9 points of the oracle blend, so it is estimable without validation data. Third, validation-free linear probes beat even the oracle-tuned blend: CLAP by +1.9 points and LP++ by +1.5 on average, and at K >= 4 all four validation-free …

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