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

Haruka Ezoe; Ryohei Hisano

cs.CLSep 25, 2026

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

Authors: Haruka Ezoe, Ryohei Hisano

Organizations: Graduate School of Information Science and Technology The University of Tokyo · The Canon Institute for Global Studies

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: CUSP turns independent period distributions into one marginal preserving temporal process. Its displacement operators yield compatible LSC readouts of magnitude and timing, mechanism, component and passage attribution, and word-local temporal modes.

Figure 2: Finite-sample recovery of (a) component parameters, (b) full, mean, and deviation operators, and (c) squared full-trace and word-local mode distances. Curves show means and

95\%

confidence intervals over

50

repetitions. Gray dashed lines show the

n^{-1/2}

rate.

Figure 4: Court localization and word-local modes. (a) Standardized adjacent change profiles for the three highest-enrichment lemmas and expectation . Diamonds mark maxima and the line is

z=1.2

. (b) Privacy modes peak in different decades. (c) The three leading expectation modes peak together. Legends give the retained mean-path energy shares. Markers and line styles distinguish series.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Notation	Meaning
Indices, spaces, and period distributions
$V,[T],d$	Vocabulary, period index set $[T]=\{1,\ldots,T\}$ , and contextual-embedding dimension.
$w,t,s,k,\ell,r$	Word, periods, period local source and target components, and word-local mode.
$\mathcal{P}_{2}(\mathbb{R}^{d}),\Pi(\mu,\nu)$	Probability measures with finite second moment, and couplings with marginals $\mu$ and $\nu$ .
$X_{t,i}^{(w)}\sim\gamma_{t}^{(w)}$	Contextual embedding of usage $i$ , sampled independently from the distribution of word $w$ in period $t$ .
$\gamma_{t}^{(w)}=\sum_{k}\pi_{t,k}^{(w)}\nu_{t,k}^{(w)}$	period specific usage distribution represented as a finite mixture.

Appendix

Table 2: Notation used in the CUSP construction, theoretical results, and experiments.

	Temporal representation			Attribution from that representation
Approach	Multi- period	Usage/component correspondence	Compositional coupling	Exact mechanism split	Transition attribution	Temporal modes
Dynamic and evolving sense models [ 6 , 7 ]	✓	✓	–	$\triangle$	–	–
WiDiD [ 32 , 8 ]	✓	✓	–	–	$\triangle$	–
Multi-period similarity analysis [ 11 ]	✓	–	–	–	–	–
SynFlow [ 33 ]	✓	$\triangle$	–	$\triangle$	$\triangle$	–
Pairwise OT [ 5 ]	$\triangle$	✓	–	–	–	–

Appendix

Table 3: Structural comparison with closely related approaches.

Panel of Figure 5 — Figure 5: Construction pipeline of the estimated semantic geometry. The pipeline maps estimated sense distributions to geometric representations. $\bullet\in\{\mathrm{full},\mathrm{mean},\mathrm{dev}\},\rho\in\{\mathrm{tr},1,\ldots,d\}$ .

Panel of Figure 6 — Figure 6: Error propagation and recovery guarantees for the estimated semantic geometry. $\bullet\in\{\mathrm{full},\mathrm{mean},\mathrm{dev}\},\rho\in\{\mathrm{tr},1,\ldots,R^{(w)}\}$ .

Quantity	Log–log slope [95% CI]	Error at $n=1600$
Prevalence $E_{\pi}$	$-0.529$ [ $-0.599,-0.458$ ]	$0.017$
Center $E_{\mu}$	$-0.437$ [ $-0.565,-0.310$ ]	$0.135$
Covariance $E_{\Sigma}$	$-0.445$ [ $-0.542,-0.348$ ]	$0.337$
Full operator $E_{M,\mathrm{full}}$	$-0.532$ [ $-0.595,-0.469$ ]	$0.570$
Mean operator $E_{M,\mathrm{mean}}$	$-0.534$ [ $-0.606,-0.463$ ]	$0.581$
Deviation operator $E_{M,\mathrm{dev}}$	$-0.514$ [ $-0.654,-0.375$ ]	$0.101$

Appendix

Table 4: Synthetic finite-sample recovery. The last column reports mean error at

n=1600

Figure 7: Squared-distance recovery for the (a) mean and (b) deviation processes. Trace and mode distances use the corresponding operator with the estimated word-local basis. Bands are

95\%

confidence intervals over

50

repetitions.

Population change	Mean term	Deviation term
Centers move	99.89 $\pm$ 0.02	0.11 $\pm$ 0.02
Covariances change	1.05 $\pm$ 0.40	98.95 $\pm$ 0.40
Prevalences change	99.95 $\pm$ 0.01	0.05 $\pm$ 0.01

Appendix

Table 5: CUSP allocation of path energy in pure-mechanism populations, in percent. Each row changes only the stated population quantity. Entries are means

\pm

95\%

confidence-interval half-widths over

20

repetitions. The theoretically correct term is bold.

	$k=0$			$k=1$			$k=3$
Language	Full	Mean	Dev.	Full	Mean	Dev.	Full	Mean	Dev.
English	$.772$	$.762$	$.673$	$.746$	$.742$	$.681$	$.762$	$.757$	$.706$
German	$.857$	$.857$	$.722$	$.815$	$.809$	$.674$	$.804$	$.798$	$.660$

Appendix

Table 6: Spearman correlation with DWUG graded-change judgments for the full, mean, and deviation traces. Each transform is fitted once to the corresponding language panel.

Schedule	$n$	Schedule recovery	Pairwise OT	CUSP
Stable	$16$	Path length $0$	$9.8\!\times\!10^{-18}$	$1.0\!\times\!10^{-17}$
Gradual	$16$	Profile TV $.044$	$.253$	$1.8\!\times\!10^{-17}$
Abrupt	$16$	Peak accuracy $1.000$	$6.4\!\times\!10^{-18}$	$1.1\!\times\!10^{-17}$
Overall	$48$	$\rho=.954$ , AUROC $1.000$	$.084$	$1.3\!\times\!10^{-17}$

Appendix

Table 7: Janus recovery with unsupervised period local GMMs and pooled panel

k=1

preprocessing. Composition error is mean

\ell_{1}

disagreement.

Quantity	Count
Distinct court opinions represented	$100{,}473$
Target lemmas	$60$
Retained passages before equalization	$322{,}222$
Passages in the balanced analysis panel	$258{,}480$
Median passages per lemma–decade	$531$
Range of equalized counts across lemmas	$294$ – $911$

Appendix

Table 8: Court corpus and balanced analysis-panel sizes. Per-decade counts are calculated after equalization within each lemma.

Rank	Lemma	Peak transition ( $z$ )	Pair	$\alpha$	$E_{\max}$
1	privacy	$1960{\to}1970$ ( $1.43$ )	$2{\to}3$	$.371$	$15.10$
2	search	$1980{\to}1990$ ( $1.55$ )	$3{\to}4$	$.690$	$13.67$
3	standing	$1960{\to}1970$ ( $1.63$ )	$3{\to}4$	$.366$	$13.23$
4	warrant	$1950{\to}1960$ ( $2.26$ )	$1{\to}0$	$.335$	$11.11$
5	trespass	$2000{\to}2010$ ( $1.74$ )	$1{\to}4$	$.390$	$10.51$
6	exercise	$1960{\to}1970$ ( $1.36$ )	$0{\to}1$	$.587$	$10.33$

Appendix

Table 9: Ten highest maximum-enrichment transitions under panel-fitted

k=1

. Contribution

\alpha

is the selected pair’s share of variation at the selected peak.

Rank	Lemma	$S_{2}$	$e_{(1)}$	$e_{(2)}$	Mode peaks
1	privacy	$.837$	$.391$	$.301$	$1960{\to}1970$ / $1950{\to}1960$
2	standing	$.788$	$.406$	$.297$	$1960{\to}1970$ / $1970{\to}1980$
3	effect	$.721$	$.452$	$.299$	$1990{\to}2000$ / $1970{\to}1980$
4	trespass	$.707$	$.359$	$.289$	$1970{\to}1980$ / $1990{\to}2000$
5	taking	$.690$	$.387$	$.360$	$2010{\to}2020$ / $2000{\to}2010$
6	due	$.683$	$.371$	$.294$	$1980{\to}1990$ / $1990{\to}2000$

Appendix

Table 10: Ten highest secondary-mode temporal-separation scores.

e_{(1)}

and

e_{(2)}

are the two leading shares among the five highest-energy mean-path modes.

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