Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change — TEI-tagged view

William L. Hamilton, Jure Leskovec, Dan Jurafsky · 2016 · digital-humanities · doi:10.18653/v1/P16-1141 · full text at the source · TEI xml · tagged edition · index · concepts · authors
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Other fields define these differently the same word, defined another way in another discipline
learning 7 fields · sample-size 5 fields · statistical-significance 2 fields · frequency 2 fields · linear regression 2 fields · semantic 2 fields · and 1 more →
Tags on this paper every tag the record carries, whether or not the words occur in the text below — a number is how many papers in the corpus carry that tag; a tag with no number is unique to this paper
word embedding10 semantic change diachronic analysis distributional semantics4 law of innovation law of conformity polysemy2 word frequency7 PPMI distributional methods co-occurrence relationships distributional hypothesis semantic similarity/distance cosine similarity/distance SVD embeddings low-dimensional approximations of the PPMI embeddings dimensionality reduction5 regularization4 SGNS ‘neural’ embeddings skip-gram with negative sampling incremental initialization Google N-Gram datasets corpus artifacts COHA corpus orthogonal Procrustes rotational alignment Pair-wise similarity time-series pairwise similarity shifts Spearman correlation7 semantic displacement cos-dist synchronic accuracy diachronic validity detecting known shifts discovering shifts from data linear mixed model3 random intercepts per word fixed effects per decade contextual diversity polysemousness empirical co-occurrence network clustering coefficient4 discourse function words controlling for frequency null model4 learning17 sociocultural conformity bias corpus-analysis16
Method, as described: computational-corpus-analysis

Our tag layer for this paper

Cross-disciplinary analysis
content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
phenomenonsemantic change— “Understanding how words change their meanings over time is key to models of language and cultural evolution, but historical data on meaning is scarce, making theories hard to develop and test.”
claim-typeexistence— “Using six historical corpora spanning four languages and two centuries, we propose two quantitative laws of semantic change: (i) the law of conformity—the rate of semantic change scales with an inverse power-law of word frequency; (ii) the law of innovation—independent of frequency, words that are more polysemous have higher rates of semantic…
method — evidence— “We then apply this methodology in a large-scale cross-linguistic analysis using 6 corpora spanning 200 years and 4 languages (English, German, French, and Chinese).”
transferfrom natural language processing (word embeddings): word embeddings (word2vec) applied across time to quantify historical semantic change— “quantifying semantic change by evaluating word embeddings (PPMI, SVD, word2vec) against known historical changes”transfers[0]
mechanismstatistical laws of semantic change: the rate of change scales as an inverse power-law of word frequency (law of conformity) and rises with polysemy (law of innovation)— “the rate of semantic change scales with an inverse power-law of word frequency”mechanisms[0]
builds-on prior distributional work on semantic change (Sagi et al., 2011; Wijaya and Yeniterzi, 2011; Gulordava and Baroni, 2011; Jatowt and Duh, 2014; Kulkarni et al., 2014; Xu and Kemp, 2015) and novel-sense detection (Lau et al., 2012; Mitra et al., 2014; Cook et al., 2014; Mitra et al., 2015; Frermann and Lapata, 2016)— “Our work builds upon a wealth of previous research on quantitative approaches to semantic change, including prior work with distributional methods (Sagi et al., 2011; Wijaya and Yeniterzi, 2011; Gulordava and Baroni, 2011; Jatowt and Duh, 2014; Kulkarni et al., 2014; Xu and Kemp, 2015), as well as recent work on detecting the emergence of…claim_relations[0]
extends the same lines of quantitative / distributional work on semantic change— “We extend these lines of work by rigorously comparing different approaches to quantifying semantic change and by using these methods to propose new statistical laws of semantic change.”claim_relations[1]
contradicts Wilkins (1993); Hopper and Traugott (2003), who argued that semantic change leads to polysemy— “However, our results show that polysemous words change faster, which suggests that polysemy may actually lead to semantic change.”claim_relations[2]
replicates Levy et al. (2015)— “These results echo the findings of Levy et al. (2015), who found SVD to perform best on similarity tasks while SGNS performed best on analogy tasks (which are not the focus of this work).”claim_relations[3]
sensethe law of innovation - TWO STATEMENTS, ONE NAME: the abstract has it holding 'independent of frequency' and the introduction 'after controlling for frequency', with 'significantly' added in the second; independence and a residual surviving adjustment are different claims, and the name that travels does not say which one is meant— “independent of frequency, words that are more polysemous have higher rates of semantic change”senses[0]
sensea rate of semantic change - A NUMBER PRODUCED BY A CHOICE OF EMBEDDING: PPMI, SVD and SGNS are ranked against each other by the paper itself, PPMI is called clearly worse and prone to false discoveries from genre shifts, and between the other two the result is equivocal - so the construct's value depends on an instrument the paper declines to settle— “PPMI is clearly worse than the other two methods; it performs poorly on all the benchmark tasks, is extremely sensitive to rare events, and is prone to false discoveries from global genre shifts. Between SVD and SGNS the results are somewhat equivocal, as both perform best on two out of the four tasks”senses[1]
sensea law - PROPOSED, NOT DERIVED: the authors say they PROPOSE two statistical laws relating frequency and polysemy to semantic change, fitted over six corpora, and the record's existing limitation already records that the analysis is correlational and the causal mechanisms are declined— “Based on this analysis, we propose two statistical laws relating frequency and polysemy to semantic change: • The law of conformity: Rates of semantic change scale with a negative power of word frequency. • The law of innovation: After controlling for frequency, polysemous words have significantly higher rates of semantic change”senses[2]
senseDistributional hypothesis - word meaning represented implicitly by co-occurrence relationships— “We use three methods to construct word embeddings within each time-period: PPMI, SVD, and SGNS (i.e., word2vec). 4 These distributional methods represent each word wi by a vector wi that captures information about its co-occurrence statistics. These methods operationalize the ‘distributional hypothesis’ that word semantics are implicit in…senses[3]
senseSVD embedding - low-dimensional regularized approximation to a PPMI representation— “SVD embeddings correspond to low-dimensional approximations of the PPMI embeddings learned via singular value decomposition (Levy et al., 2015). The vector embedding for wordwi is given by wSVD i = (UΣγ)i, (2) where MPPMI = UΣV⊤ is the truncated singular value decomposition of MPPMI and γ ∈ [0, 1] is an eigenvalue weighting parameter.…senses[4]
senseSGNS embedding - word/context vectors trained with skip-gram negative sampling— “SGNS ‘neural’ embeddings are optimized to predict co-occurrence relationships using an approximate objective known as ‘skip-gram with negative sampling’ (Mikolov et al., 2013). In SGNS, each word wi is represented by two dense, lowdimensional…senses[5]
senseGoogle N-Grams / COHA - very large artifact-prone sample versus smaller genre-balanced corpussenses[6]
senseOrthogonal Procrustes - cosine-preserving rotational alignment of embeddings across periods
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
senses[7]
sensePair-wise similarity series - changing cosine similarity summarized against time by Spearman correlation
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senses[8]
senseSemantic displacement - cosine distance between one word’s aligned representations at different times
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senses[9]
senseSynchronic accuracy / diachronic validity - within-period similarity versus across-time change performance
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senses[10]
senseDetection / discovery benchmarks - recovery of known shifts versus expert judgment of inferred shifts
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senses[11]
senseSVD / SGNS trade-off - sensitivity to subtle shifts versus robustness to corpus artifacts
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senses[12]
senseLinear mixed model - word random intercepts and decade fixed effects for displacement regression
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senses[13]
senseContextual diversity - network-neighborhood proxy for polysemousness
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senses[14]
senseLocal clustering coefficient - inverse polysemy score from co-occurrence-neighbor connectivity
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senses[15]
senseFrequency control - necessary because polysemy proxy and word frequency are intrinsically correlated
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senses[16]
senseLaw of conformity null model - frequency-driven baseline for other semantic-change interactions
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senses[17]
controlword frequency, in the law of innovation — held — rules out the reading that polysemous words change faster only because they are rarer
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controls[0]
effect directionword frequency —causes→ semantic change — reduces
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Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concept_edges[0]
weightword frequency —causes→ semantic change — 0.8
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concept_edges[0]
effect directionpolysemy —causes→ semantic change — increases
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Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concept_edges[1]
holds whenpolysemy —causes→ semantic change — after controlling for word frequency
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Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concept_edges[1]
weightpolysemy —causes→ semantic change — 0.8
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concept_edges[1]
notedistributional hypothesis —operationalised-as→ co-occurrence relationships — The paper explicitly says the methods operationalize the hypothesis through co-occurrence.
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concept_edges[2]
notesemantic similarity/distance —operationalised-as→ cosine similarity/distance — Semantic similarity/distance is approximated by cosine similarity/distance.
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concept_edges[3]
noteSVD embeddings —is-a→ low-dimensional approximations of the PPMI embeddings — The paper states SVD embeddings correspond to low-dimensional PPMI approximations.
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concept_edges[4]
notepairwise similarity shifts —operationalised-as→ Spearman correlation — Pairwise shifts are assessed with Spearman correlation against time.
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concept_edges[5]
notesemantic change —operationalised-as→ cos-dist — Cosine distance between aligned representations is explicitly used as a semantic-change measure.
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concept_edges[6]
auditSVD embeddings —contrasted-with→ SGNS ‘neural’ embeddings — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span compares the methods 'SVD' and 'SGNS', not 'SVD embeddings' / 'SGNS ‘neural’ embeddings'.
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concept_edges[7]
noteSVD embeddings —contrasted-with→ SGNS ‘neural’ embeddings — The paper contrasts SVD sensitivity with SGNS robustness and their task strengths.
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concept_edges[7]
outcome (stated by the tagger, no quotation)control — heldcontrols[0]
for which uselimitation — the mechanistic story: WHILE OUR RESULTS CANNOT CONFIRM SUCH CAUSAL LINKS, THEY NONETHELESS HIGHLIGHT A NEW ROLE FOR FREQUENCY AND POLYSEMY - correlational by the authors' own statement
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limitations[0]
for which uselimitation — every polysemy score: the measure IS SLIGHTLY BIASED TOWARDS RATING CONTEXTUALLY DIVERSE DISCOURSE FUNCTION WORDS (E.G., ALSO) AS HIGHLY POLYSEMOUS
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limitations[1]
for which uselimitation — any validation of a polysemy measure at all: MEASURING WORD POLYSEMY IS A DIFFICULT AND FRAUGHT TASK, AS EVEN 'GROUND TRUTH' DICTIONARIES DIFFER IN THE NUMBER OF SENSES THEY ASSIGN TO WORDS
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limitations[2]
for which uselimitation — every result computed on that corpus: THE GOOGLE N-GRAM DATASETS ... CONTAIN MANY CORPUS ARTIFACTS DUE, E.G., TO SHIFTING SAMPLING BIASES OVER TIME
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limitations[3]
for which uselimitation — the polysemy curvature result specifically: IT VARIES ACROSS DATASETS AND WAS NOT PRESENT WITH SGNS, SO IT IS NOT AS ROBUST AS THE CLEAR LINEAR TREND
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limitations[4]
for which uselimitation — any citation of the law of innovation: the abstract states it as holding independent of frequency, while the introduction states it as holding after controlling for frequency and adds 'significantly', and the two are not the same claim
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limitations[5]
for which uselimitation — any result computed with PPMI embeddings: the authors state
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limitations[6]
for which uselimitation — any rate of semantic change quoted from this work: between SVD and SGNS the results are described as somewhat equivocal, with each performing best on two of the four tasks
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limitations[7]
weightlearning → law of conformity — 0.4
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unhoused_relations[3]
weightsociocultural conformity bias → law of conformity — 0.4
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unhoused_relations[4]
replicationuntested
no type for thisSGNS → skip-gram with negative sampling — SGNS abbreviates skip-gram with negative sampling; acronym-expansion is absent from the edge registry.
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unhoused_relations[0]
no type for thisSVD → singular value decomposition — SVD abbreviates singular value decomposition; acronym-expansion is absent from the edge registry.
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unhoused_relations[1]
no type for thisclustering coefficient → polysemousness — A lower clustering coefficient indicates higher polysemousness; inverse-association is absent from the edge registry.
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unhoused_relations[2]
no type for thislearning → law of conformity — Learning errors are offered as a possible mechanism for the conformity law; hypothesized-mechanism-for is absent from the edge registry.
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unhoused_relations[3]
no type for thissociocultural conformity bias → law of conformity — Sociocultural conformity bias is offered as another possible mechanism; hypothesized-mechanism-for is absent from the edge registry.
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unhoused_relations[4]
no type for thisrotational alignment → orthogonal Procrustes — Orthogonal Procrustes is used to obtain rotational alignment; implemented-by is absent from the edge registry.
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unhoused_relations[5]
no type for thispolysemy → contextual diversity — Contextual diversity is used as a proxy for polysemy; proxy-for is absent from the edge registry.
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unhoused_relations[6]
limitationThe paper's results are correlational; it explicitly declines to claim the causal mechanisms it speculates about.
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limitations[0]
limitationThe polysemy proxy (local clustering coefficient in a PPMI co-occurrence network) is biased towards rating contextually diverse function words as highly polysemous.
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limitations[1]
limitationPolysemy has no agreed ground truth to validate the measure against.
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limitations[2]
limitationThe main corpora contain artifacts from shifting sampling biases over time.
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limitations[3]
limitationPart of the polysemy result (the negative curvature at high polysemy) is not robust across datasets or methods.
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limitations[4]
limitationThe paper's second law is stated in two logically different forms, two pages apart.
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limitations[5]
limitationOne of the three methods is stated to be prone to false discoveries.
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limitations[6]
limitationThe choice between the two remaining methods is left unsettled by the paper's own benchmarks.
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limitations[7]
Content tags
content-observations: finding · quantity · variable · definition · key-term — grounded in the full text
findingTwo quantitative laws of semantic change: conformity (change rate falls as an inverse power of word frequency) and innovation (more polysemous words change faster, independent of frequency).
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content_tags.findings[0]
evidence status notefinding — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted.content_tags.findings[0]
quantity6 corpora / 4 languages / 2 centuries — empirical scope of the study
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content_tags.quantities[0]
quantityinverse power-law — how semantic-change rate scales with word frequency (law of conformity)
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content_tags.quantities[1]
variableword frequency (independent)
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content_tags.variables[0]
evidence status notevariable — marked quote-not-in-current-staged-text - today's merge gate would REFUSE this quote: Paper.locate() does not find it in the current staged text.content_tags.variables[0]
not machine-vouchedvariable — not-in-our-copy - The quote is in NEITHER copy we hold - not in the text we tag against and not in the page we fetched ('fulltext.html') - checked with ligatures, hyphens, spacing and punctuation set aside. This body carries 5 detached diacritics. We do not know what it was taken from, and no class is claimed for it.content_tags.variables[0]
variablerate of semantic change (dependent)
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content_tags.variables[1]
definitionlaw of conformity
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content_tags.definitions[0]
definitionlaw of innovation
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content_tags.definitions[1]
key-termssemantic, change, word, embeddings, frequency, polysemous, diachronic, historical, corpora
Concepts
terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.
conceptsemantic change
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concepts[1]
conceptlaw of innovation
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concepts[4]
conceptlaw of conformity
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concepts[5]
conceptpolysemy
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concepts[6]
conceptword frequency
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concepts[7]
conceptPPMI
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concepts[8]
conceptdistributional methods — not defined in this paper's own words; embedding approaches representing words through co-occurrence statistics
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concepts[9]
conceptco-occurrence relationships — not defined in this paper's own words; distributional signal in which word semantics are treated as implicit
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concepts[10]
conceptdistributional hypothesis — not defined in this paper's own words; hypothesis operationalized by representing semantic information through co-occurrence
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concepts[11]
conceptsemantic similarity/distance — not defined in this paper's own words; word-level semantic proximity estimated from embedding vectors
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concepts[12]
conceptcosine similarity/distance — not defined in this paper's own words; vector measure approximating semantic similarity or distance
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concepts[13]
conceptSVD embeddings — not defined in this paper's own words; regularized low-dimensional approximations of PPMI representations
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concepts[14]
conceptlow-dimensional approximations of the PPMI embeddings — not defined in this paper's own words; compressed PPMI representations produced by singular-value decomposition
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concepts[15]
conceptdimensionality reduction — not defined in this paper's own words; SVD compression acting as regularization
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concepts[16]
conceptregularization — not defined in this paper's own words; robustness effect attributed to SVD dimensionality reduction
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concepts[17]
conceptSGNS ‘neural’ embeddings — not defined in this paper's own words; dense neural word/context vectors optimized to predict co-occurrences
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concepts[18]
conceptskip-gram with negative sampling — not defined in this paper's own words; approximate SGNS objective using negative context draws
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concepts[19]
conceptincremental initialization — not defined in this paper's own words; initializing a period’s embeddings from the preceding period
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concepts[20]
conceptGoogle N-Gram datasets — not defined in this paper's own words; very large historical book datasets with shifting-sample artifacts
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concepts[21]
conceptcorpus artifacts — not defined in this paper's own words; non-semantic shifts introduced by changing sampling and genre composition
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concepts[22]
conceptCOHA corpus — not defined in this paper's own words; smaller genre-balanced corpus representative of American English
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concepts[23]
conceptorthogonal Procrustes — not defined in this paper's own words; alignment method for historical low-dimensional embeddings
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concepts[24]
conceptrotational alignment — not defined in this paper's own words; cosine-preserving coordinate alignment across time periods
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concepts[25]
conceptPair-wise similarity time-series — not defined in this paper's own words; tracking changing cosine similarity between two words over time
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concepts[26]
conceptpairwise similarity shifts — not defined in this paper's own words; magnitude and significance of changing similarity between two words
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concepts[27]
conceptSpearman correlation — not defined in this paper's own words; nonparametric statistic measuring magnitude and significance of pairwise shifts
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concepts[28]
conceptsemantic displacement — not defined in this paper's own words; individual word’s embedding movement between time periods
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concepts[29]
conceptcos-dist — not defined in this paper's own words; distance between aligned temporal representations used as semantic-change measure
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concepts[30]
conceptsynchronic accuracy — not defined in this paper's own words; ability to capture word similarity within a single period
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concepts[31]
conceptdiachronic validity — not defined in this paper's own words; ability to quantify word-meaning changes over time
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concepts[32]
conceptdetecting known shifts — not defined in this paper's own words; benchmark asking whether known historical shifts are recovered
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concepts[33]
conceptdiscovering shifts from data — not defined in this paper's own words; benchmark judging top shifts inferred directly from data
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concepts[34]
conceptlinear mixed model — not defined in this paper's own words; regression of semantic displacement on frequency, polysemy, and time structure
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concepts[35]
conceptrandom intercepts per word — not defined in this paper's own words; word-level effects accounting for repeated measurements
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concepts[36]
conceptfixed effects per decade — not defined in this paper's own words; decade-specific terms controlling temporal trends
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concepts[37]
conceptcontextual diversity — not defined in this paper's own words; variety of unrelated usage contexts used as a polysemy proxy
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concepts[38]
conceptpolysemousness — not defined in this paper's own words; latent multiplicity of related or unrelated word senses
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concepts[39]
conceptempirical co-occurrence network — not defined in this paper's own words; PPMI graph used to measure contextual diversity
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concepts[40]
conceptclustering coefficient — not defined in this paper's own words; neighborhood statistic inversely scored as polysemy
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concepts[41]
conceptdiscourse function words — not defined in this paper's own words; contextually diverse words the proxy can over-rate as polysemous
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concepts[42]
conceptcontrolling for frequency — not defined in this paper's own words; adjustment required because contextual-diversity scores correlate with frequency
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concepts[43]
conceptnull model — not defined in this paper's own words; frequency-driven baseline for future semantic-change interactions
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concepts[44]
conceptlearning — not defined in this paper's own words; speculated route by which rare-word use errors could produce conformity
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concepts[45]
conceptsociocultural conformity bias — not defined in this paper's own words; speculated resistance to accepting innovations in common words
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concepts[46]
Statistics — cross-field join keys
field-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.
Bayesian
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content_tags.statistics[0]
evidence status noteBayesian — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted.content_tags.statistics[0]
correlation r as written: Pearson
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content_tags.statistics[1]
evidence status notecorrelation — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted.content_tags.statistics[1]
hypothesis-testing as written: test hypotheses
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content_tags.statistics[2]
statistical-significance as written: p < 0.05
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content_tags.statistics[3]
regression β as written: linear regression
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content_tags.statistics[4]
not machine-vouchedregression — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.statistics[4]
sample-size n/N as written: sample sizes
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content_tags.statistics[5]
not machine-vouchedsample-size — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.statistics[5]
statistical-significance as written: statistically significant
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content_tags.statistics[6]
variance σ²
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content_tags.statistics[7]
not machine-vouchedvariance — not-in-our-copy - The quote is in the original web page we fetched for this paper, but not in the text we tag against, which was extracted differently. Checked with ligatures, hyphens, spacing and punctuation set aside.content_tags.statistics[7]

When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.

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