# Coupled Usage-Sense Processes: Temporal and Attributable Lexical Semantic Change

arXiv: https://arxiv.org/abs/2609.30974 · HTML: https://mlsanity.com/paper/2609.30974/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change](https://mlsanity.com/paper/1605.09096/) (2016)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
- [Analysing Lexical Semantic Change with Contextualised Word Representations](https://mlsanity.com/paper/2004.14118/) (2020)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Dynamic Word Embeddings](https://mlsanity.com/paper/1702.08359/) (2017)
- [Optimal transport for Gaussian mixture models](https://mlsanity.com/paper/1710.07876/) (2017)
- [DWUG: A large Resource of Diachronic Word Usage Graphs in Four Languages](https://mlsanity.com/paper/2104.08540/) (2021)
- [A Systematic Comparison of Contextualized Word Embeddings for Lexical Semantic Change](https://mlsanity.com/paper/2402.12011/) (2024)
- [Model Selection for Gaussian Mixture Models](https://mlsanity.com/paper/1301.3558/) (2013)
- [Distribution-on-Distribution Regression with Wasserstein Metric: Multivariate Gaussian Case](https://mlsanity.com/paper/2307.06137/) (2023)
- [Investigating the Contextualised Word Embedding Dimensions Specified for Contextual and Temporal Semantic Changes](https://mlsanity.com/paper/2407.02820/) (2024)
- [SCDTour: Embedding Axis Ordering and Merging for Interpretable Semantic Change Detection](https://mlsanity.com/paper/2509.11818/) (2025)
- [Quantifying Lexical Semantic Shift via Unbalanced Optimal Transport](https://mlsanity.com/paper/2412.12569/) (2024)
- [Analyzing Continuous Semantic Shifts with Diachronic Word Similarity Matrices](https://mlsanity.com/paper/2501.09538/) (2025)
- [Word-Centered Semantic Graphs for Interpretable Diachronic Sense Tracking](https://mlsanity.com/paper/2601.22410/) (2026)
- [Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points](https://mlsanity.com/paper/2605.04589/) (2026)
- [SynFlow: A Multidimensional Diachronic Semantic Analysis Toolkit](https://mlsanity.com/paper/2608.19472/) (2026)

## Abstract (arXiv)

Lexical semantic change is usually summarized by a scalar distance between independently sampled period distributions. This measures how much a word changed, but does not reveal when it changed, which mechanisms and component movements carried the change, or which usages support the attribution. We introduce Coupled Usage--Sense Processes (CUSP), which derives these answers from a single marginal preserving temporal process. A hierarchical coupling relates contextual distributions through latent usage components, while Markov composition makes adjacent and longer span correspondences compatible. Displacement operators quantify change magnitude and timing, split variation exactly between movement of component centers and reorganization within components, and attribute it to transported component pairs. Word-local modes resolve distinct directions of change and their activity over time, while representative passages from attributed components ground the analysis in text. Under a Gaussian mixture specialization, we prove parametric recovery of the operators and squared distances. Synthetic experiments support the predicted rate. CUSP remains competitive on English and German DWUG and recovers controlled Janus profiles while maintaining compositionally coherent transport. A large corpus of US court opinions demonstrates transition, mode, and passage attribution in unlabeled natural text. CUSP thus makes magnitude, timing, mechanism, movement, modes, and textual evidence compatible views of one lexical history.