# Local Neighborhood Instability in Parametric Projections: Quantitative and Visual Analysis

arXiv: https://arxiv.org/abs/2604.21617 · HTML: https://mlsanity.com/paper/2604.21617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [Deep Learning Multidimensional Projections](https://mlsanity.com/paper/1902.07958/) (2019)
- [Verification of Neural Networks' Global Robustness](https://mlsanity.com/paper/2402.19322/) (2024)
- [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)
- [Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections](https://mlsanity.com/paper/2504.16831/) (2025)
- [Adversarial Attacks on Machine Learning-Aided Visualizations](https://mlsanity.com/paper/2409.02485/) (2024)
- [Calibrating dimension reduction hyperparameters in the presence of noise](https://mlsanity.com/paper/2312.02946/) (2023)

## Abstract (arXiv)

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely unexamined. In this paper, we present a stability evaluation framework that probes parametric projections with Gaussian perturbations around selected anchor points and assesses how neighborhoods deform in the 2D embedding. Our approach combines quantitative measures of mean displacement, bias, and nearest-anchor assignment error with per-anchor visualizations of displacement vectors, local PCA ellipsoids, and Voronoi misassignment for detailed inspection. We demonstrate the framework's effectiveness on UMAP- and t-SNE-based neural projectors of varying network sizes and study the effect of Jacobian regularization as a gradient-based robustness strategy. We apply our framework to the MNIST and Fashion-MNIST datasets. The results show that our framework identifies unstable projection regions invisible to reconstruction error or neighborhood-preservation metrics.