# Adaptive Poincar'e Point to Set Distance for Few-Shot Classification

arXiv: https://arxiv.org/abs/2112.01719 · HTML: https://mlsanity.com/paper/2112.01719/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 55 references that are in the map.
- First posted on arXiv 3 Dec 2021.

## Builds on (most cited first, 30 of 39)

- [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)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [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)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (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)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [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)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learning](https://mlsanity.com/paper/1911.04623/) (2019)
- [CrossTransformers: spatially-aware few-shot transfer](https://mlsanity.com/paper/2007.11498/) (2020)
- [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)
- [Adversarial Feature Hallucination Networks for Few-Shot Learning](https://mlsanity.com/paper/2003.13193/) (2020)
- [Finding Task-Relevant Features for Few-Shot Learning by Category Traversal](https://mlsanity.com/paper/1905.11116/) (2019)
- [Meta-Learning with Warped Gradient Descent](https://mlsanity.com/paper/1909.00025/) (2019)
- [When Does Self-supervision Improve Few-shot Learning?](https://mlsanity.com/paper/1910.03560/) (2019)
- [Partial Is Better Than All: Revisiting Fine-tuning Strategy for Few-shot Learning](https://mlsanity.com/paper/2102.03983/) (2021)

## Built on by (most cited first, 15 of 15)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Rethinking Generalization in Few-Shot Classification](https://mlsanity.com/paper/2206.07267/) (2022)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [Curved Geometric Networks for Visual Anomaly Recognition](https://mlsanity.com/paper/2208.01188/) (2022)
- [RankDNN: Learning to Rank for Few-shot Learning](https://mlsanity.com/paper/2211.15320/) (2022)
- [Learning Instance and Task-Aware Dynamic Kernels for Few Shot Learning](https://mlsanity.com/paper/2112.03494/) (2021)
- [Hyperbolic Geometry in Computer Vision: A Survey](https://mlsanity.com/paper/2304.10764/) (2023)
- [When Cars meet Drones: Hyperbolic Federated Learning for Source-Free Domain Adaptation in Adverse Weather](https://mlsanity.com/paper/2403.13762/) (2024)
- [Few-shot Classification via Ensemble Learning with Multi-Order Statistics](https://mlsanity.com/paper/2305.00454/) (2023)
- [Compositional Prototypical Networks for Few-Shot Classification](https://mlsanity.com/paper/2306.06584/) (2023)
- [Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors](https://mlsanity.com/paper/2506.10146/) (2025)
- [Rethinking the Sample Relations for Few-Shot Classification](https://mlsanity.com/paper/2501.13418/) (2025)
- [State Space Models for Extractive Summarization in Low Resource Scenarios](https://mlsanity.com/paper/2501.14673/) (2025)
- [A Set-to-Set Distance Measure in Hyperbolic Space](https://mlsanity.com/paper/2506.18529/) (2025)

## Abstract (arXiv)

Learning and generalizing from limited examples, i,e, few-shot learning, is of core importance to many real-world vision applications. A principal way of achieving few-shot learning is to realize an embedding where samples from different classes are distinctive. Recent studies suggest that embedding via hyperbolic geometry enjoys low distortion for hierarchical and structured data, making it suitable for few-shot learning. In this paper, we propose to learn a context-aware hyperbolic metric to characterize the distance between a point and a set associated with a learned set to set distance. To this end, we formulate the metric as a weighted sum on the tangent bundle of the hyperbolic space and develop a mechanism to obtain the weights adaptively and based on the constellation of the points. This not only makes the metric local but also dependent on the task in hand, meaning that the metric will adapt depending on the samples that it compares. We empirically show that such metric yields robustness in the presence of outliers and achieves a tangible improvement over baseline models. This includes the state-of-the-art results on five popular few-shot classification benchmarks, namely mini-ImageNet, tiered-ImageNet, Caltech-UCSD Birds-200-2011 (CUB), CIFAR-FS, and FC100.