# Advances in Set Function Learning: A Survey of Techniques and Applications

arXiv: https://arxiv.org/abs/2501.14991 · HTML: https://mlsanity.com/paper/2501.14991/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 90 of its 153 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Builds on (most cited first, 30 of 90)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Asymmetric Loss For Multi-Label Classification](https://mlsanity.com/paper/2009.14119/) (2020)
- [PIXOR: Real-time 3D Object Detection from Point Clouds](https://mlsanity.com/paper/1902.06326/) (2019)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [3D-MPA: Multi Proposal Aggregation for 3D Semantic Instance Segmentation](https://mlsanity.com/paper/2003.13867/) (2020)

## Built on by (most cited first, 3 of 3)

- [CheMixHub: Datasets and Benchmarks for Chemical Mixture Property Prediction](https://mlsanity.com/paper/2506.12231/) (2025)
- [Scalable Single-Cell Gene Expression Generation with Latent Diffusion Models](https://mlsanity.com/paper/2511.02986/) (2025)
- [On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets](https://mlsanity.com/paper/2505.24403/) (2025)

## Abstract (arXiv)

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of features matters, set function learning demands methods that are invariant to permutations of the input set, presenting a unique and complex problem. This survey provides a comprehensive overview of the current development in set function learning, covering foundational theories, key methodologies, and diverse applications. We categorize and discuss existing approaches, focusing on deep learning approaches, such as DeepSets and Set Transformer based methods, as well as other notable alternative methods beyond deep learning, offering a complete view of current models. We also introduce various applications and relevant datasets, such as point cloud processing and multi-label classification, highlighting the significant progress achieved by set function learning methods in these domains. Finally, we conclude by summarizing the current state of set function learning approaches and identifying promising future research directions, aiming to guide and inspire further advancements in this promising field.