# Rep the Set: Neural Networks for Learning Set Representations

arXiv: https://arxiv.org/abs/1904.01962 · HTML: https://mlsanity.com/paper/1904.01962/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

## Built on by (most cited first, 22 of 22)

- [Learning Prototype-oriented Set Representations for Meta-Learning](https://mlsanity.com/paper/2110.09140/) (2021)
- [Re-evaluating Word Mover's Distance](https://mlsanity.com/paper/2105.14403/) (2021)
- [Label-Free Model Evaluation with Semi-Structured Dataset Representations](https://mlsanity.com/paper/2112.00694/) (2021)
- [Set-to-Sequence Methods in Machine Learning: a Review](https://mlsanity.com/paper/2103.09656/) (2021)
- [Set Representation Learning with Generalized Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2103.03892/) (2021)
- [RecipeMind: Guiding Ingredient Choices from Food Pairing to Recipe Completion using Cascaded Set Transformer](https://mlsanity.com/paper/2210.10628/) (2022)
- [Toward Auto-evaluation with Confidence-based Category Relation-aware Regression](https://mlsanity.com/paper/2304.08288/) (2023)
- [SeTformer is What You Need for Vision and Language](https://mlsanity.com/paper/2401.03540/) (2024)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [DuMLP-Pin: A Dual-MLP-dot-product Permutation-invariant Network for Set Feature Extraction](https://mlsanity.com/paper/2203.04007/) (2022)
- [Set Interdependence Transformer: Set-to-Sequence Neural Networks for Permutation Learning and Structure Prediction](https://mlsanity.com/paper/2206.03720/) (2022)
- [Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classification](https://mlsanity.com/paper/2306.05553/) (2023)
- [Hawk: An Industrial-strength Multi-label Document Classifier](https://mlsanity.com/paper/2301.06057/) (2023)
- [Learning Permutation-invariant Macroscopic Dynamics](https://mlsanity.com/paper/2605.30812/) (2026)
- [On Inductive Biases for Machine Learning in Data Constrained Settings](https://mlsanity.com/paper/2302.10692/) (2023)
- [Set2Seq Transformer: Temporal and Position-Aware Set Representations for Sequential Multiple-Instance Learning](https://mlsanity.com/paper/2408.03404/) (2024)
- [A QUBO Framework for Team Formation](https://mlsanity.com/paper/2503.23209/) (2025)
- [On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets](https://mlsanity.com/paper/2505.24403/) (2025)
- [Wasserstein Hypergraph Neural Network](https://mlsanity.com/paper/2506.09682/) (2025)
- [Improving Set Function Approximation with Quasi-Arithmetic Neural Networks](https://mlsanity.com/paper/2602.04941/) (2026)
- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)
- [Integrating Fairness and Explainability in a Multiple Instance Reinforcement Learning System](https://mlsanity.com/paper/2610.00035/) (2026)

## Abstract (arXiv)

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this kind of representations, since sets may vary in cardinality and elements lack a meaningful ordering. In this paper, we present a new neural network architecture, called RepSet, that can handle examples that are represented as sets of vectors. The proposed model computes the correspondences between an input set and some hidden sets by solving a series of network flow problems. This representation is then fed to a standard neural network architecture to produce the output. The architecture allows end-to-end gradient-based learning. We demonstrate RepSet on classification tasks, including text categorization, and graph classification, and we show that the proposed neural network achieves performance better or comparable to state-of-the-art algorithms.