# Tracking Temporal Dynamics of Vector Sets with Gaussian Process

arXiv: https://arxiv.org/abs/2512.15538 · HTML: https://mlsanity.com/paper/2512.15538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change](https://mlsanity.com/paper/1605.09096/) (2016)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [SemEval-2020 Task 1: Unsupervised Lexical Semantic Change Detection](https://mlsanity.com/paper/2007.11464/) (2020)
- [Evaluating the Underlying Gender Bias in Contextualized Word Embeddings](https://mlsanity.com/paper/1904.08783/) (2019)
- [Statistically Significant Detection of Linguistic Change](https://mlsanity.com/paper/1411.3315/) (2014)
- [PSTNet: Point Spatio-Temporal Convolution on Point Cloud Sequences](https://mlsanity.com/paper/2205.13713/) (2022)
- [Unsupervised Semantic Variation Prediction using the Distribution of Sibling Embeddings](https://mlsanity.com/paper/2305.08654/) (2023)
- [Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck](https://mlsanity.com/paper/2309.07200/) (2023)
- [Partial Wasserstein Adversarial Network for Non-rigid Point Set Registration](https://mlsanity.com/paper/2203.02227/) (2022)
- [Investigating the Contextualised Word Embedding Dimensions Specified for Contextual and Temporal Semantic Changes](https://mlsanity.com/paper/2407.02820/) (2024)

## Abstract (arXiv)

Understanding the temporal evolution of sets of vectors is a fundamental challenge across various domains, including ecology, crime analysis, and linguistics. For instance, ecosystem structures evolve due to interactions among plants, herbivores, and carnivores; the spatial distribution of crimes shifts in response to societal changes; and word embedding vectors reflect cultural and semantic trends over time. However, analyzing such time-varying sets of vectors is challenging due to their complicated structures, which also evolve over time. In this work, we propose a novel method for modeling the distribution underlying each set of vectors using infinite-dimensional Gaussian processes. By approximating the latent function in the Gaussian process with Random Fourier Features, we obtain compact and comparable vector representations over time. This enables us to track and visualize temporal transitions of vector sets in a low-dimensional space. We apply our method to both sociological data (crime distributions) and linguistic data (word embeddings), demonstrating its effectiveness in capturing temporal dynamics. Our results show that the proposed approach provides interpretable and robust representations, offering a powerful framework for analyzing structural changes in temporally indexed vector sets across diverse domains.