# Towards General-Purpose Representation Learning of Polygonal Geometries

arXiv: https://arxiv.org/abs/2209.15458 · HTML: https://mlsanity.com/paper/2209.15458/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 84 references that are in the map.
- First posted on arXiv 29 Sep 2022.

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

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Deep Layer Aggregation](https://mlsanity.com/paper/1707.06484/) (2017)
- [A Neural Representation of Sketch Drawings](https://mlsanity.com/paper/1704.03477/) (2017)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Efficient Interactive Annotation of Segmentation Datasets with Polygon-RNN++](https://mlsanity.com/paper/1803.09693/) (2018)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [PolyTransform: Deep Polygon Transformer for Instance Segmentation](https://mlsanity.com/paper/1912.02801/) (2019)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [Annotating Object Instances with a Polygon-RNN](https://mlsanity.com/paper/1704.05548/) (2017)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [LSTM-TrajGAN: A Deep Learning Approach to Trajectory Privacy Protection](https://mlsanity.com/paper/2006.10521/) (2020)

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

- [On the Opportunities and Challenges of Foundation Models for Geospatial Artificial Intelligence](https://mlsanity.com/paper/2304.06798/) (2023)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023)
- [TorchSpatial: A Location Encoding Framework and Benchmark for Spatial Representation Learning](https://mlsanity.com/paper/2406.15658/) (2024)
- [MapQA: Open-domain Geospatial Question Answering on Map Data](https://mlsanity.com/paper/2503.07871/) (2025)
- [Poly2Vec: Polymorphic Fourier-Based Encoding of Geospatial Objects for GeoAI Applications](https://mlsanity.com/paper/2408.14806/) (2024)
- [PolygonGNN: Representation Learning for Polygonal Geometries with Heterogeneous Visibility Graph](https://mlsanity.com/paper/2407.00742/) (2024)
- [Transformation vs Tradition: Artificial General Intelligence (AGI) for Arts and Humanities](https://mlsanity.com/paper/2310.19626/) (2023)
- [Geo2Vec: Shape- and Distance-Aware Neural Representation of Geospatial Entities](https://mlsanity.com/paper/2508.19305/) (2025)
- [EVKG: An Interlinked and Interoperable Electric Vehicle Knowledge Graph for Smart Transportation System](https://mlsanity.com/paper/2304.04893/) (2023)
- [S2Vec: Self-Supervised Geospatial Embeddings for the Built Environment](https://mlsanity.com/paper/2504.16942/) (2025)
- [Training-free Spatially Grounded Geometric Shape Encoding (Technical Report)](https://mlsanity.com/paper/2604.07522/) (2026)
- [Spatial Representation Learning Beyond Pixels: Unifying Raster Data and Vector Semantics for Human-Centric Geospatial Foundation Models](https://mlsanity.com/paper/2606.02374/) (2026)
- [Inferring High-level Geographical Concepts via Knowledge Graph and Multi-scale Data Integration: A Case Study of C-shaped Building Pattern Recognition](https://mlsanity.com/paper/2304.09391/) (2023)
- [Learning Geometric Invariant Features for Classification of Vector Polygons with Graph Message-passing Neural Network](https://mlsanity.com/paper/2407.04334/) (2024)
- [Omni Geometry Representation Learning vs Large Language Models for Geospatial Entity Resolution](https://mlsanity.com/paper/2508.06584/) (2025)
- [TrajGANR: Trajectory-Centric Urban Multimodal Learning via Geospatially Aligned Neural Representations](https://mlsanity.com/paper/2605.06990/) (2026)
- [NARA: Anchor-Conditioned Representation Learning for Heterogeneous Vector Geoentities](https://mlsanity.com/paper/2605.12276/) (2026)
- [Geometry-Aware Reinforcement Learning for 2D Irregular Nesting](https://mlsanity.com/paper/2606.10611/) (2026)
- [Automated Quality Assessment of Geospatial Vector Data: A GeoAI Approach using Spatial Representation Learning](https://mlsanity.com/paper/2606.28390/) (2026)
- [PolyTopoBench: A Benchmark for Complex Vector Polygon Generation from Remote Sensing Imagery](https://mlsanity.com/paper/2609.32856/) (2026)
- [Geospatial Vector Geometry as a Native Spatial Modality for Vision-Language Models](https://mlsanity.com/paper/2610.16769/) (2026)

## Abstract (arXiv)

Neural network representation learning for spatial data is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and networks, whereas little progress has been made for polygons, especially complex polygonal geometries. In this work, we focus on developing a general-purpose polygon encoding model, which can encode a polygonal geometry (with or without holes, single or multipolygons) into an embedding space. The result embeddings can be leveraged directly (or finetuned) for downstream tasks such as shape classification, spatial relation prediction, and so on. To achieve model generalizability guarantees, we identify a few desirable properties: loop origin invariance, trivial vertex invariance, part permutation invariance, and topology awareness. We explore two different designs for the encoder: one derives all representations in the spatial domain; the other leverages spectral domain representations. For the spatial domain approach, we propose ResNet1D, a 1D CNN-based polygon encoder, which uses circular padding to achieve loop origin invariance on simple polygons. For the spectral domain approach, we develop NUFTspec based on Non-Uniform Fourier Transformation (NUFT), which naturally satisfies all the desired properties. We conduct experiments on two tasks: 1) shape classification based on MNIST; 2) spatial relation prediction based on two new datasets - DBSR-46K and DBSR-cplx46K. Our results show that NUFTspec and ResNet1D outperform multiple existing baselines with significant margins. While ResNet1D suffers from model performance degradation after shape-invariance geometry modifications, NUFTspec is very robust to these modifications due to the nature of the NUFT.