# Learning Prototype-oriented Set Representations for Meta-Learning

arXiv: https://arxiv.org/abs/2110.09140 · HTML: https://mlsanity.com/paper/2110.09140/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 57 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 30 of 38)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)
- [Few-Shot Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1905.01723/) (2019)
- [Attend, Infer, Repeat: Fast Scene Understanding with Generative Models](https://mlsanity.com/paper/1603.08575/) (2016)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [CondenseNet: An Efficient DenseNet using Learned Group Convolutions](https://mlsanity.com/paper/1711.09224/) (2017)
- [Towards a Neural Statistician](https://mlsanity.com/paper/1606.02185/) (2016)
- [Infinite Mixture Prototypes for Few-Shot Learning](https://mlsanity.com/paper/1902.04552/) (2019)
- [On Learning Sets of Symmetric Elements](https://mlsanity.com/paper/2002.08599/) (2020)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [FIGR: Few-shot Image Generation with Reptile](https://mlsanity.com/paper/1901.02199/) (2019)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [F2GAN: Fusing-and-Filling GAN for Few-shot Image Generation](https://mlsanity.com/paper/2008.01999/) (2020)
- [DAWSON: A Domain Adaptive Few Shot Generation Framework](https://mlsanity.com/paper/2001.00576/) (2020)
- [MatchingGAN: Matching-based Few-shot Image Generation](https://mlsanity.com/paper/2003.03497/) (2020)

## Built on by (most cited first, 19 of 19)

- [Morphological Prototyping for Unsupervised Slide Representation Learning in Computational Pathology](https://mlsanity.com/paper/2405.11643/) (2024)
- [Multimodal Prototyping for cancer survival prediction](https://mlsanity.com/paper/2407.00224/) (2024)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [POUF: Prompt-oriented unsupervised fine-tuning for large pre-trained models](https://mlsanity.com/paper/2305.00350/) (2023)
- [Tuning Multi-mode Token-level Prompt Alignment across Modalities](https://mlsanity.com/paper/2309.13847/) (2023)
- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)
- [Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transport](https://mlsanity.com/paper/2210.04144/) (2022)
- [Neural Collapse Terminus: A Unified Solution for Class Incremental Learning and Its Variants](https://mlsanity.com/paper/2308.01746/) (2023)
- [Learning to Rematch Mismatched Pairs for Robust Cross-Modal Retrieval](https://mlsanity.com/paper/2403.05105/) (2024)
- [LLM Reading Tea Leaves: Automatically Evaluating Topic Models with Large Language Models](https://mlsanity.com/paper/2406.09008/) (2024)
- [Neural Topic Modeling with Large Language Models in the Loop](https://mlsanity.com/paper/2411.08534/) (2024)
- [Enhancing Unsupervised Graph Few-shot Learning via Set Functions and Optimal Transport](https://mlsanity.com/paper/2501.05635/) (2025)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [Regularized Optimal Transport Layers for Generalized Global Pooling Operations](https://mlsanity.com/paper/2212.06339/) (2022)
- [Robust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learning](https://mlsanity.com/paper/2602.01427/) (2026)
- [Towards Context-Aware Domain Generalization: Understanding the Benefits and Limits of Marginal Transfer Learning](https://mlsanity.com/paper/2312.10107/) (2023)
- [Investigating Mask-aware Prototype Learning for Tabular Anomaly Detection](https://mlsanity.com/paper/2506.02757/) (2025)
- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)
- [Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation](https://mlsanity.com/paper/2610.00678/) (2026)

## Abstract (arXiv)

Learning from set-structured data is a fundamental problem that has recently attracted increasing attention, where a series of summary networks are introduced to deal with the set input. In fact, many meta-learning problems can be treated as set-input tasks. Most existing summary networks aim to design different architectures for the input set in order to enforce permutation invariance. However, scant attention has been paid to the common cases where different sets in a meta-distribution are closely related and share certain statistical properties. Viewing each set as a distribution over a set of global prototypes, this paper provides a novel prototype-oriented optimal transport (POT) framework to improve existing summary networks. To learn the distribution over the global prototypes, we minimize its regularized optimal transport distance to the set empirical distribution over data points, providing a natural unsupervised way to improve the summary network. Since our plug-and-play framework can be applied to many meta-learning problems, we further instantiate it to the cases of few-shot classification and implicit meta generative modeling. Extensive experiments demonstrate that our framework significantly improves the existing summary networks on learning more powerful summary statistics from sets and can be successfully integrated into metric-based few-shot classification and generative modeling applications, providing a promising tool for addressing set-input and meta-learning problems.