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

arXiv: https://arxiv.org/abs/2309.01256 · HTML: https://mlsanity.com/paper/2309.01256/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 56 of its 73 references that are in the map.
- First posted on arXiv 3 Sep 2023.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 56)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Conditional Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2203.05557/) (2022)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [Grounded Language-Image Pre-training](https://mlsanity.com/paper/2112.03857/) (2021)
- [CLIP-Adapter: Better Vision-Language Models with Feature Adapters](https://mlsanity.com/paper/2110.04544/) (2021)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Florence: A New Foundation Model for Computer Vision](https://mlsanity.com/paper/2111.11432/) (2021)
- [PaLI: A Jointly-Scaled Multilingual Language-Image Model](https://mlsanity.com/paper/2209.06794/) (2022)
- [SimVLM: Simple Visual Language Model Pretraining with Weak Supervision](https://mlsanity.com/paper/2108.10904/) (2021)
- [Image as a Foreign Language: BEiT Pretraining for All Vision and Vision-Language Tasks](https://mlsanity.com/paper/2208.10442/) (2022)
- [Less is More: ClipBERT for Video-and-Language Learning via Sparse Sampling](https://mlsanity.com/paper/2102.06183/) (2021)
- [Test-Time Prompt Tuning for Zero-Shot Generalization in Vision-Language Models](https://mlsanity.com/paper/2209.07511/) (2022)
- [Tip-Adapter: Training-free Adaption of CLIP for Few-shot Classification](https://mlsanity.com/paper/2207.09519/) (2022)
- [Prompt-aligned Gradient for Prompt Tuning](https://mlsanity.com/paper/2205.14865/) (2022)

## Built on by (most cited first, 6 of 6)

- [Learning to Adapt CLIP for Few-Shot Monocular Depth Estimation](https://mlsanity.com/paper/2311.01034/) (2023)
- [Concept-Guided Prompt Learning for Generalization in Vision-Language Models](https://mlsanity.com/paper/2401.07457/) (2024)
- [Learning Visual Conditioning Tokens to Correct Domain Shift for Fully Test-time Adaptation](https://mlsanity.com/paper/2406.19341/) (2024)
- [Dual-Path Adversarial Lifting for Domain Shift Correction in Online Test-time Adaptation](https://mlsanity.com/paper/2408.13983/) (2024)
- [Support-Set Context Matters for Bongard Problems](https://mlsanity.com/paper/2309.03468/) (2023)
- [Domain-Conditioned Transformer for Fully Test-time Adaptation](https://mlsanity.com/paper/2410.10442/) (2024)

## Abstract (arXiv)

Large-scale pre-trained Vision-Language Models (VLMs), such as CLIP and ALIGN, have introduced a new paradigm for learning transferable visual representations. Recently, there has been a surge of interest among researchers in developing lightweight fine-tuning techniques to adapt these models to downstream visual tasks. We recognize that current state-of-the-art fine-tuning methods, such as Tip-Adapter, simply consider the covariance between the query image feature and features of support few-shot training samples, which only captures linear relations and potentially instigates a deceptive perception of independence. To address this issue, in this work, we innovatively introduce Brownian Distance Covariance (BDC) to the field of vision-language reasoning. The BDC metric can model all possible relations, providing a robust metric for measuring feature dependence. Based on this, we present a novel method called BDC-Adapter, which integrates BDC prototype similarity reasoning and multi-modal reasoning network prediction to perform classification tasks. Our extensive experimental results show that the proposed BDC-Adapter can freely handle non-linear relations and fully characterize independence, outperforming the current state-of-the-art methods by large margins.