# Polyra Swarms: A Shape-Based Approach to Machine Learning

arXiv: https://arxiv.org/abs/2506.13217 · HTML: https://mlsanity.com/paper/2506.13217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Deep Learning for Person Re-identification: A Survey and Outlook](https://mlsanity.com/paper/2001.04193/) (2020)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Analysis of Explainers of Black Box Deep Neural Networks for Computer Vision: A Survey](https://mlsanity.com/paper/1911.12116/) (2019)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Fast MCMC sampling algorithms on polytopes](https://mlsanity.com/paper/1710.08165/) (2017)
- [Empirical comparison between autoencoders and traditional dimensionality reduction methods](https://mlsanity.com/paper/2103.04874/) (2021)
- [Meta-survey on outlier and anomaly detection](https://mlsanity.com/paper/2312.07101/) (2023)
- [The Geometric Occam's Razor Implicit in Deep Learning](https://mlsanity.com/paper/2111.15090/) (2021)
- [Does Deep Learning Learn to Abstract? A Systematic Probing Framework](https://mlsanity.com/paper/2302.11978/) (2023)
- [Bounding Box Disparity: 3D Metrics for Object Detection With Full Degree of Freedom](https://mlsanity.com/paper/2207.03720/) (2022)

## Abstract (arXiv)

We propose Polyra Swarms, a novel machine-learning approach that approximates shapes instead of functions. Our method enables general-purpose learning with very low bias. In particular, we show that depending on the task, Polyra Swarms can be preferable compared to neural networks, especially for tasks like anomaly detection. We further introduce an automated abstraction mechanism that simplifies the complexity of a Polyra Swarm significantly, enhancing both their generalization and transparency. Since Polyra Swarms operate on fundamentally different principles than neural networks, they open up new research directions with distinct strengths and limitations.