# DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy

arXiv: https://arxiv.org/abs/2508.12145 · HTML: https://mlsanity.com/paper/2508.12145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 16 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Deep Learning Multidimensional Projections](https://mlsanity.com/paper/1902.07958/) (2019)
- [UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data](https://mlsanity.com/paper/2111.01744/) (2021)
- [Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections](https://mlsanity.com/paper/2504.16831/) (2025)
- [Uncertainty-Aware Principal Component Analysis](https://mlsanity.com/paper/1905.01127/) (2019)

## Abstract (arXiv)

Recently, autoencoders (AEs) have gained interest for creating parametric and invertible projections of multidimensional data. Parametric projections make it possible to embed new, unseen samples without recalculating the entire projection, while invertible projections allow the synthesis of new data instances. However, existing methods perform poorly when dealing with out-of-distribution samples in either the data or embedding space. Thus, we propose DE-VAE, an uncertainty-aware variational AE using differential entropy (DE) to improve the learned parametric and invertible projections. Given a fixed projection, we train DE-VAE to learn a mapping into 2D space and an inverse mapping back to the original space. We conduct quantitative and qualitative evaluations on four well-known datasets, using UMAP and t-SNE as baseline projection methods. Our findings show that DE-VAE can create parametric and inverse projections with comparable accuracy to other current AE-based approaches while enabling the analysis of embedding uncertainty.