# Joint Distribution Matters: Deep Brownian Distance Covariance for Few-Shot Classification

arXiv: https://arxiv.org/abs/2204.04567 · HTML: https://mlsanity.com/paper/2204.04567/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 64 references that are in the map.
- First posted on arXiv 9 Apr 2022.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [Rethinking Few-Shot Image Classification: a Good Embedding Is All You Need?](https://mlsanity.com/paper/2003.11539/) (2020)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [A Baseline for Few-Shot Image Classification](https://mlsanity.com/paper/1909.02729/) (2019)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [DropBlock: A regularization method for convolutional networks](https://mlsanity.com/paper/1810.12890/) (2018)
- [Cross-Domain Few-Shot Classification via Learned Feature-Wise Transformation](https://mlsanity.com/paper/2001.08735/) (2020)
- [Meta-Baseline: Exploring Simple Meta-Learning for Few-Shot Learning](https://mlsanity.com/paper/2003.04390/) (2020)
- [CrossTransformers: spatially-aware few-shot transfer](https://mlsanity.com/paper/2007.11498/) (2020)
- [Charting the Right Manifold: Manifold Mixup for Few-shot Learning](https://mlsanity.com/paper/1907.12087/) (2019)
- [Negative Margin Matters: Understanding Margin in Few-shot Classification](https://mlsanity.com/paper/2003.12060/) (2020)
- [Revisiting Local Descriptor based Image-to-Class Measure for Few-shot Learning](https://mlsanity.com/paper/1903.12290/) (2019)
- [Few-Shot Classification with Feature Map Reconstruction Networks](https://mlsanity.com/paper/2012.01506/) (2020)
- [Finding Task-Relevant Features for Few-Shot Learning by Category Traversal](https://mlsanity.com/paper/1905.11116/) (2019)
- [Laplacian Regularized Few-Shot Learning](https://mlsanity.com/paper/2006.15486/) (2020)
- [Delta-encoder: an effective sample synthesis method for few-shot object recognition](https://mlsanity.com/paper/1806.04734/) (2018)
- [Associative Alignment for Few-shot Image Classification](https://mlsanity.com/paper/1912.05094/) (2019)

## Built on by (most cited first, 30 of 50)

- [A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunities](https://mlsanity.com/paper/2205.06743/) (2022)
- [Rethinking Generalization in Few-Shot Classification](https://mlsanity.com/paper/2206.07267/) (2022)
- [HQG-Net: Unpaired Medical Image Enhancement with High-Quality Guidance](https://mlsanity.com/paper/2307.07829/) (2023)
- [Few-Shot Learning Meets Transformer: Unified Query-Support Transformers for Few-Shot Classification](https://mlsanity.com/paper/2208.12398/) (2022)
- [ProtoDiff: Learning to Learn Prototypical Networks by Task-Guided Diffusion](https://mlsanity.com/paper/2306.14770/) (2023)
- [Reference Twice: A Simple and Unified Baseline for Few-Shot Instance Segmentation](https://mlsanity.com/paper/2301.01156/) (2023)
- [An Embarrassingly Simple Approach to Semi-Supervised Few-Shot Learning](https://mlsanity.com/paper/2209.13777/) (2022)
- [Boosting Few-Shot Learning via Attentive Feature Regularization](https://mlsanity.com/paper/2403.17025/) (2024)
- [Envisioning Class Entity Reasoning by Large Language Models for Few-shot Learning](https://mlsanity.com/paper/2408.12469/) (2024)
- [MVP: Meta Visual Prompt Tuning for Few-Shot Remote Sensing Image Scene Classification](https://mlsanity.com/paper/2309.09276/) (2023)
- [Making Large Vision Language Models to be Good Few-shot Learners](https://mlsanity.com/paper/2408.11297/) (2024)
- [BDC-Adapter: Brownian Distance Covariance for Better Vision-Language Reasoning](https://mlsanity.com/paper/2309.01256/) (2023)
- [Causality-Driven One-Shot Learning for Prostate Cancer Grading from MRI](https://mlsanity.com/paper/2309.10725/) (2023)
- [MetaCoCo: A New Few-Shot Classification Benchmark with Spurious Correlation](https://mlsanity.com/paper/2404.19644/) (2024)
- [Few-shot Fine-grained Image Classification via Multi-Frequency Neighborhood and Double-cross Modulation](https://mlsanity.com/paper/2207.08547/) (2022)
- [SpatialFormer: Semantic and Target Aware Attentions for Few-Shot Learning](https://mlsanity.com/paper/2303.09281/) (2023)
- [Clustered-patch Element Connection for Few-shot Learning](https://mlsanity.com/paper/2304.10093/) (2023)
- [Task-Oriented Channel Attention for Fine-Grained Few-Shot Classification](https://mlsanity.com/paper/2308.00093/) (2023)
- [Few-shot Classification via Ensemble Learning with Multi-Order Statistics](https://mlsanity.com/paper/2305.00454/) (2023)
- [Disentangled Representation Learning with Transmitted Information Bottleneck](https://mlsanity.com/paper/2311.01686/) (2023)
- [PM2: A New Prompting Multi-modal Model Paradigm for Few-shot Medical Image Classification](https://mlsanity.com/paper/2404.08915/) (2024)
- [Few-shot Classification with Hypersphere Modeling of Prototypes](https://mlsanity.com/paper/2211.05319/) (2022)
- [An Adaptive Plug-and-Play Network for Few-Shot Learning](https://mlsanity.com/paper/2302.09326/) (2023)
- [FILM: How can Few-Shot Image Classification Benefit from Pre-Trained Language Models?](https://mlsanity.com/paper/2307.04114/) (2023)
- [Adaptive receptive field-based spatial-frequency feature reconstruction network for fine-grained few-shot image classification](https://mlsanity.com/paper/2604.16936/) (2026)
- [SpurAudio: A Benchmark for Studying Shortcut Learning in Few-Shot Audio Classification](https://mlsanity.com/paper/2605.13672/) (2026)
- [Boosting Meta-Training with Base Class Information for Few-Shot Learning](https://mlsanity.com/paper/2403.03472/) (2024)
- [Task Attribute Distance for Few-Shot Learning: Theoretical Analysis and Applications](https://mlsanity.com/paper/2403.03535/) (2024)
- [Boosting Few-Shot Learning with Disentangled Self-Supervised Learning and Meta-Learning for Medical Image Classification](https://mlsanity.com/paper/2403.17530/) (2024)
- [Intra-task Mutual Attention based Vision Transformer for Few-Shot Learning](https://mlsanity.com/paper/2405.03109/) (2024)

## Abstract (arXiv)

Few-shot classification is a challenging problem as only very few training examples are given for each new task. One of the effective research lines to address this challenge focuses on learning deep representations driven by a similarity measure between a query image and few support images of some class. Statistically, this amounts to measure the dependency of image features, viewed as random vectors in a high-dimensional embedding space. Previous methods either only use marginal distributions without considering joint distributions, suffering from limited representation capability, or are computationally expensive though harnessing joint distributions. In this paper, we propose a deep Brownian Distance Covariance (DeepBDC) method for few-shot classification. The central idea of DeepBDC is to learn image representations by measuring the discrepancy between joint characteristic functions of embedded features and product of the marginals. As the BDC metric is decoupled, we formulate it as a highly modular and efficient layer. Furthermore, we instantiate DeepBDC in two different few-shot classification frameworks. We make experiments on six standard few-shot image benchmarks, covering general object recognition, fine-grained categorization and cross-domain classification. Extensive evaluations show our DeepBDC significantly outperforms the counterparts, while establishing new state-of-the-art results. The source code is available at http://www.peihuali.org/DeepBDC