# The Balanced-Pairwise-Affinities Feature Transform

arXiv: https://arxiv.org/abs/2407.01467 · HTML: https://mlsanity.com/paper/2407.01467/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [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)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Deep Learning for Person Re-identification: A Survey and Outlook](https://mlsanity.com/paper/2001.04193/) (2020)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [A Baseline for Few-Shot Image Classification](https://mlsanity.com/paper/1909.02729/) (2019)
- [Omni-Scale Feature Learning for Person Re-Identification](https://mlsanity.com/paper/1905.00953/) (2019)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [Re-ranking Person Re-identification with k-reciprocal Encoding](https://mlsanity.com/paper/1701.08398/) (2017)
- [Style Transfer by Relaxed Optimal Transport and Self-Similarity](https://mlsanity.com/paper/1904.12785/) (2019)
- [Sinkformers: Transformers with Doubly Stochastic Attention](https://mlsanity.com/paper/2110.11773/) (2021)
- [Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference](https://mlsanity.com/paper/2204.07305/) (2022)
- [SPICE: Semantic Pseudo-labeling for Image Clustering](https://mlsanity.com/paper/2103.09382/) (2021)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [On Learning Sets of Symmetric Elements](https://mlsanity.com/paper/2002.08599/) (2020)

## Built on by (most cited first, 2 of 2)

- [RoNFA: Robust Neural Field-based Approach for Few-Shot Image Classification with Noisy Labels](https://mlsanity.com/paper/2506.03461/) (2025)
- [ViT-ProtoNet for Few-Shot Image Classification: A Multi-Benchmark Evaluation](https://mlsanity.com/paper/2507.09299/) (2025)

## Abstract (arXiv)

The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order relations between the input features. A particular min-cost-max-flow fractional matching problem, whose entropy regularized version can be approximated by an optimal transport (OT) optimization, leads to a transform which is efficient, differentiable, equivariant, parameterless and probabilistically interpretable. While the Sinkhorn OT solver has been adapted extensively in many contexts, we use it differently by minimizing the cost between a set of features to itself and using the transport plan's rows as the new representation. Empirically, the transform is highly effective and flexible in its use and consistently improves networks it is inserted into, in a variety of tasks and training schemes. We demonstrate state-of-the-art results in few-shot classification, unsupervised image clustering and person re-identification. Code is available at urlgithub.com/DanielShalam/BPA.