Gahl & Baayen (2024): English homophone duration via DLM

@cite{gahl-baayen-2024} @cite{baayen-2019} @cite{heitmeier-chuang-baayen-2026}

Gahl, S., & Baayen, R. H. (2024). Time and thyme again: Connecting English spoken word duration to models of the mental lexicon. Language 100(4), 623–670.

Empirical claims

The paper reanalyses the Switchboard-corpus homophone-duration data of Gahl 2008 (409 English homophone pairs such as time / thyme, side / sighed) and asks whether a discriminative-lexicon (DL) model without stored words can recover the homophone duration effect — long attributed to lexical frequency. The headline findings:

1. Form-meaning isomorphism predicts homophone duration differences. The duration of a homophone correlates with how strongly its meaning supports its form (paper §5.2 Table 4). The semantic support measure outperforms lexical frequency in a Gaussian location-scale GAMM (DL-based AIC −239.13 vs. localist AIC −231.69; evidence ratio 41.26 in paper Table 5).
2. Homophone semantic similarity predicts duration similarity. Pearson correlation of homophone-pair semantic vectors is a significant predictor of how close their durations are (paper §5.2 Table 4). Semantically similar homophones are produced more similarly, consistent with the DL prediction that meaning → form mappings vary continuously with the meaning input.
3. Contextual independence (CIND) outperforms frequency. A novel measure derived from a word-to-word matrix W (satisfying UW = U for utterance multi-hot matrix U) captures how much a word's meaning can be inferred independently of its utterance context. Replacing lemma frequency with CIND consistently improves model fit (paper §5.3 Table 5).

The substantive theoretical move: lexical frequency is composite, not primitive. The "frequency effect" on duration decomposes into (a) practice/learning (operationalised via Frequency-Informed Learning of the mapping G), (b) contextual independence (CIND), and (c) semantic support for form (SemSupForm). A model without stored lexical entries can recover the duration patterns previously attributed to frequency.

Substrate (this file)

This is the fourth consumer of the LinearDiscriminativeLexicon substrate (Theories/Processing/Lexical/Discriminative/Defs.lean), after ChuangEtAl2026, LuChuangBaayen2026, and Saito2025. It is also the second consumer of the semSup family (after Saito 2025), the consumer that triggered the semSup/semSupWord lift to Measures.lean (CHANGELOG 0.231.18).

Carrier instantiation: 5,600-dim binary triphone vectors × 200-dim fastText English embeddings (paper §3.4, appendix §A2). The substrate is dimension-polymorphic; only the dimensions and the empirical training data differ from Saito's German setup.

Substrate generality validated (cumulative table)

Axis	Chuang 2026	Lu 2026	Saito 2025	Gahl-B 2024
Language	Mandarin	Mandarin	German	English
Modality	f0 pitch	f0 pitch	EMA tongue pos.	acoustic duration
Form rep	50-dim ℝ	100-dim ℝ	14,404-dim binary	5,600-dim binary
Meaning rep	768-dim CKIP	768-dim CKIP	300-dim word2vec	200-dim fastText
Phenomenon	tonal realiz.	tone sandhi	morpho-phonetics	homophone duration
Headline measure	word smooth	sense smooth	semSupSuffix	semSupForm + CIND

Same LinearDiscriminativeLexicon ℝ FormVec MeaningVec accommodates all four with carrier-type instantiation only — no specialisation.

Cross-paper convergence

The four DLM Studies share a common architectural commitment that this file makes especially explicit: the seemingly pretheoretical construct "lexical frequency" decomposes into separable distributional facts (paper §1.1, §6.4). Three of the four (Chuang, Lu, Saito) make this point implicitly by demonstrating word-or-meaning predictors that subsume frequency effects; Gahl & Baayen 2024 makes it the explicit headline. Lu's tone sandhi and Saito's morphological-boundary effects are both special cases of this composite-frequency story.

Cross-framework note: localist (WEAVER, Dell) vs DL

The paper directly compares DL-based GAMMs to GAMMs grounded in localist lexical models (Dell 1986, Levelt-Roelofs-Meyer 1999) where frequency is a property of stored lexical entries. linglib does not currently formalize WEAVER or Dell-style spreading-activation substrates; the cross-framework discrimination lives in this file's prose (§5 below). When a Theories/Processing/Lexical/WEAVER/ sibling lands, the localist–DL comparison can become a Lean-stateable contrast theorem.

Sections

• §1 Substrate instantiation (English DLM at 5600/200 dimensions)
• §2 Paper-specific alias for word-level semantic support
• §3 Lipschitz application: similar homophone meanings ⇒ similar predicted forms
• §4 Empirical content (prose; includes CIND and HomophoneSemSim)

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.GahlBaayen2024.EnglishTriphoneCount : ℕ

Number of triphones in the paper's CELEX-derived word-by-triphone matrix C (paper appendix §A2: matrix C of shape 10,636 × 5,600). Form vectors are zero/one binary indicators of triphone presence.

Equations

• Phenomena.Phonology.Studies.GahlBaayen2024.EnglishTriphoneCount = 5600

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.GahlBaayen2024.FastTextEnglishDim : ℕ

Dimensionality of the pretrained fastText English embeddings (paper appendix §A2: matrix S of shape 10,636 × 200; the embeddings are the tweet-based fastText vectors cited in the paper).

Equations

• Phenomena.Phonology.Studies.GahlBaayen2024.FastTextEnglishDim = 200

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.GahlBaayen2024.EnglishTriphoneVec : Type

A form vector for the English DLM. The "binary" structure is data, not type — FormVec is Fin n → ℝ.

Equations

• Phenomena.Phonology.Studies.GahlBaayen2024.EnglishTriphoneVec = Theories.Processing.Lexical.Discriminative.FormVec Phenomena.Phonology.Studies.GahlBaayen2024.EnglishTriphoneCount

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.GahlBaayen2024.EnglishFastTextVec : Type

A semantic vector: 200-dim fastText embedding of word meaning.

Equations

• Phenomena.Phonology.Studies.GahlBaayen2024.EnglishFastTextVec = Theories.Processing.Lexical.Discriminative.MeaningVec Phenomena.Phonology.Studies.GahlBaayen2024.FastTextEnglishDim

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.GahlBaayen2024.EnglishHomophoneDLM : Type

The paper's specific DLM instantiation.

Equations

• One or more equations did not get rendered due to their size.

@[reducible, inline]

noncomputable abbrev Phenomena.Phonology.Studies.GahlBaayen2024.semSupForm (D : EnglishHomophoneDLM) (s : EnglishFastTextVec) (triphones : List (Fin EnglishTriphoneCount)) : ℝ

Semantic Support for Form (paper §3.4 eq. 10): the total support a word's meaning provides to its constituent triphones, Σ_{j ∈ word} (D.production s) j. The paper's name for the semSupWord measure (now in Theories/Processing/Lexical/Discriminative/Measures.lean); here as an abbrev re-exporting under the paper-specific name.

Two other paper-specific measures (CIND for contextual independence, HomophoneSemSim for Pearson correlation of homophone-pair semantic vectors) are defined in the paper but not formalised as Lean defs in this file. CIND requires formalising the word-to-word matrix W satisfying UW = U (paper §3.2 eq. 9 — substantial substrate work). HomophoneSemSim requires inner-product / Pearson machinery on MeaningVec (deferred to a future Measures/InnerProduct.lean sibling). Both measures are recorded in §4 prose.

Equations

• Phenomena.Phonology.Studies.GahlBaayen2024.semSupForm D s triphones = Theories.Processing.Lexical.Discriminative.semSupWord D s triphones

theorem Phenomena.Phonology.Studies.GahlBaayen2024.homophone_similarity_implies_form_similarity (D : EnglishHomophoneDLM) (s₁ s₂ : EnglishFastTextVec) {ε : ℝ} (h : ‖s₁ - s₂‖ ≤ ε) : ‖D.production s₁ - D.production s₂‖ ≤ ‖LinearMap.toContinuousLinearMap D.production‖ * ε

Quantitative form of the homophone-similarity → duration-similarity prediction (paper §3.4, §5.2). The paper reports that homophone pairs with high homophoneSemSim (semantically similar meanings) have more similar durations.

Structurally, this follows from the Lipschitz continuity of the production map: if two semantic vectors are close, their predicted form vectors are close, which (given that triphone presences feed duration estimation) implies close predicted durations.

Direct application of dlm_neighbor_centroids_imply_neighbor_contours to the English homophone DLM. The fourth consumer of this Lipschitz theorem (after Chuang, Lu, Saito), validating it as DLM-substrate- canonical.

Findings as paper-supplied empirical facts

Per CLAUDE.md (Processing-scope guidance), specific GAMM fits, AIC deltas, and random forest variable-importance scores are out of scope as Lean theorems. They are recorded here as documented findings.

DL-based GAMM outperforms localist GAMM (paper §5.2 / §5.3, Tables 3-5). Three Gaussian-location-scale GAMMs fitted to log-duration of 409 Switchboard homophones:

• Localist (predictors: lemma frequency, relative frequency, phonological neighbourhood density, +controls): AIC = −231.69.
• DL with frequency-informed-learning (FIL) semSupForm + CIND +HomophoneSemSim +controls: AIC = −239.13. Best DL model: endstate-learning semSupForm + CIND + ortho consistency → AIC = −244.77 (evidence ratio 692.29 vs. localist baseline; paper Table 5).

SemSupForm with endstate learning is the strongest predictor (paper §5.4, Fig. 5). Random Forest variable importance ranks LogSemanticSupportFormEOL highest, ahead of phonological neighbourhood density, orthographic regularity, lemma frequency, and CIND. The endstate-learning variant is preferred for variable-importance analysis because it is uncorrelated with frequency (r ≈ −0.38, vs r = +0.61 for the FIL variant).

Homophones do NOT sound identical (paper §6.1, §1.3 — confirmed contra prior reanalyses claiming the effect is artefactual). Confirmed: the duration of time differs from the duration of thyme even when speaker, phonetic-segment baseline, prosodic position, and noun-bias are controlled for. The DL model explains this via meaning: identical triphone vectors but different semantic vectors → different predicted form vectors via D.production → different duration estimates.

Frequency is composite (paper §1.1, §6.4 — the headline theoretical claim). The DL predictors practice (FIL), contextual independence (CIND), and semantic support for form (SemSupForm) jointly capture what was previously bundled under "frequency". The "frequency effect" decomposes; no stored lexical entry need carry a frequency property.

Implications recorded in the paper's discussion

• Anti-lexical-storage (paper §6.1, §6.2 contra @cite{levelt-roelofs-meyer-1999} and the Dell-style spreading- activation lineage): frequency effects on duration emerge from a model without stored words. The DL model has only the matrices C, S, and the trained mappings G, F, W — no lexical entries bearing frequency annotations.
• Form-meaning isomorphism (paper §6.3, §6.4): the linear mapping G : S → C predicts considerable structural alignment between the semantic and form spaces — a generalisation of sound-symbolism / iconicity beyond onomatopoeia and ideophones. Quantitatively validated by the homophone-similarity → duration-similarity prediction (§3 above).
• Contextual independence as cognitive measure (paper §3.2, §6.4): CIND captures how much a word's meaning can be learned without its co-occurring contexts, and is correlated with visual lexical decision times (paper appendix §A5.1, validated against the British Lexicon Project).
• Convergence with @cite{saito-tomaschek-baayen-2025}: both papers find that DL-derived semantic-support measures replace categorical morphological / lexical predictors with smaller AIC values and (in Saito) fewer effective degrees of freedom. The composite-frequency thesis of paper §6.4 receives independent support from the German morpho-phonetics data of Saito 2025.