# Topological Obstructions to Autoencoding

arXiv: https://arxiv.org/abs/2102.08380 · HTML: https://mlsanity.com/paper/2102.08380/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 81 references that are in the map.
- First posted on arXiv 16 Feb 2021.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Don't Decay the Learning Rate, Increase the Batch Size](https://mlsanity.com/paper/1711.00489/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [A Neural Scaling Law from the Dimension of the Data Manifold](https://mlsanity.com/paper/2004.10802/) (2020)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)
- [Variational Autoencoders for Anomalous Jet Tagging](https://mlsanity.com/paper/2007.01850/) (2020)
- [QCD-Aware Recursive Neural Networks for Jet Physics](https://mlsanity.com/paper/1702.00748/) (2017)
- [Deep learning in color: towards automated quark/gluon jet discrimination](https://mlsanity.com/paper/1612.01551/) (2016)
- [Novelty Detection Meets Collider Physics](https://mlsanity.com/paper/1807.10261/) (2018)
- [Linearized Optimal Transport for Collider Events](https://mlsanity.com/paper/2008.08604/) (2020)
- [Jet Constituents for Deep Neural Network Based Top Quark Tagging](https://mlsanity.com/paper/1704.02124/) (2017)
- [Long Short-Term Memory (LSTM) networks with jet constituents for boosted top tagging at the LHC](https://mlsanity.com/paper/1711.09059/) (2017)
- [Recursive Neural Networks in Quark/Gluon Tagging](https://mlsanity.com/paper/1711.02633/) (2017)
- [Autoencoding topology](https://mlsanity.com/paper/1803.00156/) (2018)
- [Jet Charge and Machine Learning](https://mlsanity.com/paper/1803.08066/) (2018)
- [Deep Neural Networks for Physics Analysis on low-level whole-detector data at the LHC](https://mlsanity.com/paper/1711.03573/) (2017)
- [Opening the black box of neural nets: case studies in stop/top discrimination](https://mlsanity.com/paper/1804.09278/) (2018)

## Built on by (most cited first, 20 of 20)

- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Autoencoders for unsupervised anomaly detection in high energy physics](https://mlsanity.com/paper/2104.09051/) (2021)
- [Learning Topology-Preserving Data Representations](https://mlsanity.com/paper/2302.00136/) (2023)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [Better Latent Spaces for Better Autoencoders](https://mlsanity.com/paper/2104.08291/) (2021)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Comparing Weak- and Unsupervised Methods for Resonant Anomaly Detection](https://mlsanity.com/paper/2104.02092/) (2021)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [ELSA -- Enhanced latent spaces for improved collider simulations](https://mlsanity.com/paper/2305.07696/) (2023)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)
- [Why should autoencoders work?](https://mlsanity.com/paper/2310.02250/) (2023)
- [Dynamical transition in controllable quantum neural networks with large depth](https://mlsanity.com/paper/2311.18144/) (2023)
- [Improving the performance of weak supervision searches using transfer and meta-learning](https://mlsanity.com/paper/2312.06152/) (2023)
- [Autoencoding Dynamics: Topological Limitations and Capabilities](https://mlsanity.com/paper/2511.04807/) (2025)
- [TRANSIT your events into a new mass: Fast background interpolation for weakly-supervised anomaly searches](https://mlsanity.com/paper/2503.04342/) (2025)
- [Geometry-Preserving Neural Architectures on Manifolds with Boundary](https://mlsanity.com/paper/2602.03082/) (2026)
- [Generative models on phase space](https://mlsanity.com/paper/2604.02415/) (2026)
- [Contrastive Learning for Interpretable Anomaly Detection at Collider Experiments](https://mlsanity.com/paper/2608.13652/) (2026)

## Abstract (arXiv)

Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of n-particle phase space.