# Learning minimal representations of stochastic processes with variational autoencoders

arXiv: https://arxiv.org/abs/2307.11608 · HTML: https://mlsanity.com/paper/2307.11608/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 21 Jul 2023.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Recurrent Memory Transformer](https://mlsanity.com/paper/2207.06881/) (2022)
- [fastai: A Layered API for Deep Learning](https://mlsanity.com/paper/2002.04688/) (2020)
- [DARLA: Improving Zero-Shot Transfer in Reinforcement Learning](https://mlsanity.com/paper/1707.08475/) (2017)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Unsupervised speech representation learning using WaveNet autoencoders](https://mlsanity.com/paper/1901.08810/) (2019)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Dynamics-aware Embeddings](https://mlsanity.com/paper/1908.09357/) (2019)
- [Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning](https://mlsanity.com/paper/1907.06011/) (2019)
- [Computer-inspired Quantum Experiments](https://mlsanity.com/paper/2002.09970/) (2020)
- [Operationally meaningful representations of physical systems in neural networks](https://mlsanity.com/paper/2001.00593/) (2020)
- [Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data](https://mlsanity.com/paper/2011.03474/) (2020)
- [Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning](https://mlsanity.com/paper/2003.01504/) (2020)
- [Unsupervised learning of anomalous diffusion data](https://mlsanity.com/paper/2108.03411/) (2021)

## Built on by (most cited first, 7 of 7)

- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator](https://mlsanity.com/paper/2509.13821/) (2025)
- [Machine Learning Analysis of Anomalous Diffusion](https://mlsanity.com/paper/2412.01393/) (2024)
- [Discovering quantum phenomena with Interpretable Machine Learning](https://mlsanity.com/paper/2604.16015/) (2026)
- [Discover physical concepts and equations with machine learning](https://mlsanity.com/paper/2412.12161/) (2024)
- [Global graph features unveiled by unsupervised geometric deep learning](https://mlsanity.com/paper/2503.05560/) (2025)
- [Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectories](https://mlsanity.com/paper/2512.08510/) (2025)

## Abstract (arXiv)

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended β-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.