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Large-scale pre-trained Vision-Language Models (VLMs), such as CLIP andALIGN, have introduced a new paradigm for learning transferable visualrepresentations. Recently, there has been a surge of interest among researchersin developing lightweight fine-tuning techniques to adapt these models todownstream visual tasks. We recognize that current state-of-the-art fine-tuningmethods, such as Tip-Adapter, simply consider the covariance between the queryimage feature and features of support few-shot training samples, which onlycaptures linear relations and potentially instigates a deceptive perception ofindependence. To address this issue, in this work, we innovatively introduceBrownian Distance Covariance (BDC) to the field of vision-language reasoning.The BDC metric can model all possible relations, providing a robust metric formeasuring feature dependence. Based on this, we present a novel method calledBDC-Adapter, which integrates BDC prototype similarity reasoning andmulti-modal reasoning network prediction to perform classification tasks. Ourextensive experimental results show that the proposed BDC-Adapter can freelyhandle non-linear relations and fully characterize independence, outperformingthe current state-of-the-art methods by large margins.

BDC-Adapter: Brownian Distance Covariance for Better Vision-Language Reasoning