# Anomaly Detection in Aeronautics Data with Quantum-compatible Discrete Deep Generative Model

arXiv: https://arxiv.org/abs/2303.12302 · HTML: https://mlsanity.com/paper/2303.12302/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 92 references that are in the map.
- First posted on arXiv 22 Mar 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Discrete Variational Autoencoders](https://mlsanity.com/paper/1609.02200/) (2016)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Adversarially Learned Anomaly Detection](https://mlsanity.com/paper/1812.02288/) (2018)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [MuProp: Unbiased Backpropagation for Stochastic Neural Networks](https://mlsanity.com/paper/1511.05176/) (2015)
- [DVAE++: Discrete Variational Autoencoders with Overlapping Transformations](https://mlsanity.com/paper/1802.04920/) (2018)
- [Scaling Memory-Augmented Neural Networks with Sparse Reads and Writes](https://mlsanity.com/paper/1610.09027/) (2016)

## Built on by (most cited first, 1 of 1)

- [Quantum Enhanced Anomaly Detection for ADS-B Data using Hybrid Deep Learning](https://mlsanity.com/paper/2509.15991/) (2025)

## Abstract (arXiv)

Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models -- variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors -- in detecting anomalies in flight-operations data of commercial flights consisting of multivariate time series. We devised two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. The DVAE with RBM prior, using a relatively simple -- and classically or quantum-mechanically enhanceable -- sampling technique for the evolution of the RBM's negative phase, performed better than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection tasks. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device.