# Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transport

arXiv: https://arxiv.org/abs/2210.04144 · HTML: https://mlsanity.com/paper/2210.04144/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 62 references that are in the map.
- First posted on arXiv 9 Oct 2022.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [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)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Dynamic Few-Shot Visual Learning without Forgetting](https://mlsanity.com/paper/1804.09458/) (2018)
- [Feature Generating Networks for Zero-Shot Learning](https://mlsanity.com/paper/1712.00981/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Low-Shot Learning from Imaginary Data](https://mlsanity.com/paper/1801.05401/) (2018)
- [Free Lunch for Few-shot Learning: Distribution Calibration](https://mlsanity.com/paper/2101.06395/) (2021)
- [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)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Delta-encoder: an effective sample synthesis method for few-shot object recognition](https://mlsanity.com/paper/1806.04734/) (2018)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Few-Shot Learning with Embedded Class Models and Shot-Free Meta Training](https://mlsanity.com/paper/1905.04398/) (2019)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Neural Topic Model via Optimal Transport](https://mlsanity.com/paper/2008.13537/) (2020)
- [An Ensemble of Epoch-wise Empirical Bayes for Few-shot Learning](https://mlsanity.com/paper/1904.08479/) (2019)

## Built on by (most cited first, 14 of 14)

- [Hierarchical Vector Quantized Transformer for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2310.14228/) (2023)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Tuning Multi-mode Token-level Prompt Alignment across Modalities](https://mlsanity.com/paper/2309.13847/) (2023)
- [Uncertainty-Aware Optimal Transport for Semantically Coherent Out-of-Distribution Detection](https://mlsanity.com/paper/2303.10449/) (2023)
- [Enhancing CLIP Robustness via Cross-Modality Alignment](https://mlsanity.com/paper/2510.24038/) (2025)
- [Dynamic Multimodal Prototype Learning in Vision-Language Models](https://mlsanity.com/paper/2507.03657/) (2025)
- [Prototypes-oriented Transductive Few-shot Learning with Conditional Transport](https://mlsanity.com/paper/2308.03047/) (2023)
- [Look Carefully: Adaptive Visual Reinforcements in Multimodal Large Language Models for Hallucination Mitigation](https://mlsanity.com/paper/2602.24041/) (2026)
- [Enhancing Unsupervised Graph Few-shot Learning via Set Functions and Optimal Transport](https://mlsanity.com/paper/2501.05635/) (2025)
- [Covariance-based Space Regularization for Few-shot Class Incremental Learning](https://mlsanity.com/paper/2411.01172/) (2024)
- [Robust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learning](https://mlsanity.com/paper/2602.01427/) (2026)
- [CALA: A Class-Aware Logit Adapter for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2412.12654/) (2024)
- [GuardAlign: Test-time Safety Alignment in Multimodal Large Language Models](https://mlsanity.com/paper/2602.24027/) (2026)
- [Investigating Mask-aware Prototype Learning for Tabular Anomaly Detection](https://mlsanity.com/paper/2506.02757/) (2025)

## Abstract (arXiv)

Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the low-level OT, which considers the weights of all the data samples in the base class. Experimental results on standard benchmarks demonstrate that our proposed plug-and-play model outperforms competing approaches and owns desired cross-domain generalization ability, indicating the effectiveness of the learned adaptive weights.