Vision-language models such as CLIP and SigLIP provide strong zero-shot recognition, but their predictions can degrade when deployed on target data that differ from the pretraining distribution. Test-time adaptation offers a practical way to improve robustness without source data or target labels, yet existing methods often rely on either prompt-side adaptation or image-side target evidence alone. In this work, we introduce GATE, a training-free two-pass transductive test-time adaptation framework that uses the unlabeled target set while keeping the image encoder, text encoder, and prompt parameters fully frozen. Instead of representing each class with a single prototype, GATE builds two complementary Gaussian sources of evidence in the shared vision-language feature space: a text Gaussian estimated from multiple language descriptions and an image Gaussian estimated from reliable unlabeled target samples. A class-wise reliability gate controls the influence of image-derived pseudo-evidence, and a score-level generalized Product-of-Experts fusion produces a normalized residual correction to the original zero-shot logits. Across fine-grained recognition datasets, ImageNet-family distribution shifts, multiple CLIP backbones, and SigLIP-B/16, GATE achieves the best average accuracy in every benchmark/backbone group. It improves zero-shot performance by an average of 5.41 points and outperforms the strongest non-GATE baseline by 1.94 points, demonstrating the benefit of reliability-gated distributional evidence for frozen VLM adaptation.

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