# Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections

arXiv: https://arxiv.org/abs/2504.16831 · HTML: https://mlsanity.com/paper/2504.16831/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 23 Apr 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)
- [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)
- [HyperNP: Interactive Visual Exploration of Multidimensional Projection Hyperparameters](https://mlsanity.com/paper/2106.13777/) (2021)
- [ParaDime: A Framework for Parametric Dimensionality Reduction](https://mlsanity.com/paper/2210.04582/) (2022)
- [Interactive Counterfactual Generation for Univariate Time Series](https://mlsanity.com/paper/2408.10633/) (2024)

## Built on by (most cited first, 4 of 4)

- [FloDR: An invertible dimensionality reduction method based on a normalising flow](https://mlsanity.com/paper/2607.26278/) (2026)
- [DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy](https://mlsanity.com/paper/2508.12145/) (2025)
- [LCIP: Loss-Controlled Inverse Projection of High-Dimensional Image Data](https://mlsanity.com/paper/2602.11141/) (2026)
- [Local Neighborhood Instability in Parametric Projections: Quantitative and Visual Analysis](https://mlsanity.com/paper/2604.21617/) (2026)

## Abstract (arXiv)

Recently, neural networks have gained attention for creating parametric and invertible multidimensional data projections. Parametric projections allow for embedding previously unseen data without recomputing the projection as a whole, while invertible projections enable the generation of new data points. However, these properties have never been explored simultaneously for arbitrary projection methods. We evaluate three autoencoder (AE) architectures for creating parametric and invertible projections. Based on a given projection, we train AEs to learn a mapping into 2D space and an inverse mapping into the original space. We perform a quantitative and qualitative comparison on four datasets of varying dimensionality and pattern complexity using t-SNE. Our results indicate that AEs with a customized loss function can create smoother parametric and inverse projections than feed-forward neural networks while giving users control over the strength of the smoothing effect.