Saito, Tomaschek & Baayen (2025): Frequency × inflectional status via DLM

@cite{saito-tomaschek-baayen-2025} @cite{baayen-2019} @cite{heitmeier-chuang-baayen-2026}

Saito, M., Tomaschek, F., & Baayen, R. H. (2025). Interaction of frequency and inflectional status: An approach from discriminative learning. Preprint v1.

Empirical claims

The paper investigates the apparent contradiction between two documented frequency effects on phonetic realization:

• Phonetic reduction: high-frequency words have shorter durations, more centralized formants, more raised tongue positions (@cite{aylett-turk-2004} smooth signal redundancy hypothesis + several earlier corpus and ultrasound studies cited in paper §1).
• Phonetic enhancement: high-frequency morphologically complex words show longer/clearer realizations (paradigmatic enhancement literature, paper §1).

The study reanalyses German tongue position data (560 word tokens, 88 word types containing the rhyme [a(:)…t] from the Karl-Eberhard Corpus of spontaneous southern German) and finds:

1. Inflectional status × frequency interaction: high-frequency non-inflected words show tongue raising (reduction); high- frequency inflected words show attenuated reduction (paper §2.2, Tables 1–2).
2. DLM-derived semantic support replaces the binary morphological predictor: replacing the categorical InflStatus factor with the continuous SemSupSuffix measure (semantic support from word meaning to the suffix triphone, derived from the trained DLM) improves model fit by 142.87 AIC units (paper §3.3, Table 3).
3. Architectural challenge to WEAVER++: the result undermines speech production models that posit intermediate symbolic morphological representations (@cite{levelt-roelofs-meyer-1999} and the Roelofs WEAVER lineage). Form ↔ meaning mappings without a morpheme layer suffice.

The substantive theoretical move: what looks like a morphological- boundary effect is driven by inflectional semantics.

Substrate (this file)

This file is the third consumer of the LinearDiscriminativeLexicon substrate (Theories/Processing/Lexical/Discriminative/Defs.lean), after @cite{chuang-bell-tseng-baayen-2026} and @cite{lu-chuang-baayen-2026}. It validates the polymorphic carrier typing across every axis of variation:

Axis	Chuang 2026	Lu 2026	Saito 2025
Language	Mandarin	Mandarin	German
Modality	f0 pitch	f0 pitch	EMA tongue position
Form rep	50-dim ℝ	100-dim ℝ	14,404-dim binary
Meaning rep	768-dim CKIP	768-dim CKIP	300-dim word2vec
Phenomenon	tonal realiz.	tone sandhi	morpho-phonetics

The same LinearDiscriminativeLexicon ℝ FormVec MeaningVec instantiates to all three. The "binary" structure of form vectors here (zero/one triphone presence) is a property of the training data the network sees, not of the type — Fin 14404 → ℝ accommodates {0,1}-valued sequences as a special case.

SemSup measures (substrate)

The paper introduces a family of derived measures (paper §3.1) on top of a trained DLM: SemSup, SemSupVowel, SemSupSuffix, SemSupWord, PredAcc, FuncLoad, SemLen, UncertProd, UncertComp. The first four are paper-headline; the rest are diagnostic.

The general measures (semSup, semSupWord) plus their linearity lemmas live in Theories/Processing/Lexical/Discriminative/Measures.lean, having graduated to substrate when @cite{gahl-baayen-2024} landed as a second consumer. The paper-specific positional variants (semSupVowel, semSupSuffix) stay here as abbrevs wrapping the substrate primitive.

Cross-framework note: WEAVER++ challenged but unformalized

The paper's headline architectural claim — that no intermediate morpheme layer is needed between semantics and articulation — directly challenges WEAVER++ (@cite{levelt-roelofs-meyer-1999} and the broader WEAVER lineage). linglib does not currently formalize WEAVER++; the cross-framework discrimination would require a Theories/Processing/Lexical/WEAVER/ sibling that explicitly posits a lemma layer. Defer until a second WEAVER-using study lands.

Sibling-framework engagement

Like the Chuang and Lu DLM Studies, this file's claims sit in tension with the stored-lexicon assumptions in:

• Theories/Phonology/ItemSpecificity/{UseListed, IndexedConstraints, RepresentationStrength, ScaledWeights}.lean — four phonological frequency-channel theories, all of which posit stored entries to attach frequency to. Saito's frequency × inflectional-status interaction is the phenomenon those channels would compete to explain; the DLM offers a 5th, no-stored-entries account.
• Theories/Morphology/UsageBased/Network.lean (@cite{bybee-1985}): Bybee's tokenFreq : Nat is the canonical stored-frequency primitive; the DLM's production linear map dispenses with it.

Phenomena/Phonology/Studies/BreissKatsudaKawahara2026.lean is the closest sibling phenomenon — Japanese morpho-phonetics with explicit discrimination among the four ItemSpecificity channels. Saito's DLM analysis would form a natural 5th line in that paper's discrimination table; the structural cross-framework theorem is deferred until a unified LexiconArchitecture typeclass exists (per the cross-framework reconciler's recommendation, see CHANGELOG 0.231.15).

Sections

• §1 Substrate instantiation (German DLM at 14404/300 dimensions)
• §2 Paper-specific semSup aliases (vowel/suffix variants)
• §3 Lipschitz application to articulation
• §4 Empirical content (prose)

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.TriphoneCount : ℕ

The full set of triphones in the paper's CELEX-derived word-by- triphone matrix (paper §3.1: matrix C of shape 64068 × 14404). Form vectors are zero/one binary indicators of triphone presence.

Equations

• Phenomena.Phonology.Studies.Saito2025.TriphoneCount = 14404

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.Word2VecGermanDim : ℕ

The dimensionality of the pretrained word2vec German embeddings (paper §3.1: matrix S of shape 64068 × 300; paper cites the German word2vec model of Müller 2015 — bib entry omitted).

Equations

• Phenomena.Phonology.Studies.Saito2025.Word2VecGermanDim = 300

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.TriphoneVec : Type

A form vector: zero/one indicator of which triphones the word contains. The "binary" structure is data, not type — FormVec is Fin n → ℝ and binary vectors are a subset.

Equations

• Phenomena.Phonology.Studies.Saito2025.TriphoneVec = Theories.Processing.Lexical.Discriminative.FormVec Phenomena.Phonology.Studies.Saito2025.TriphoneCount

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.GermanWord2VecVec : Type

A semantic vector: 300-dim word2vec embedding of word meaning.

Equations

• Phenomena.Phonology.Studies.Saito2025.GermanWord2VecVec = Theories.Processing.Lexical.Discriminative.MeaningVec Phenomena.Phonology.Studies.Saito2025.Word2VecGermanDim

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.GermanInflectionalDLM : Type

The paper's specific DLM instantiation. The substrate type LinearDiscriminativeLexicon is in Theories/Processing/Lexical/Discriminative/Defs.lean; this abbreviation specialises it to the German triphone × word2vec dimensions.

Equations

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

SemSupVowel and SemSupSuffix (paper §3.1 eq. 3, 4)

The general measures semSup and semSupWord (with linearity lemmas) live in Theories/Processing/Lexical/Discriminative/Measures.lean. The two positional variants below are paper-specific bindings naming which triphone index is being projected. abbrev for transparency (simp / rw see through to semSup).

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.semSupVowel (D : GermanInflectionalDLM) (s : GermanWord2VecVec) (vowelTriphoneIdx : Fin TriphoneCount) : ℝ

SemSupVowel (paper §3.1 eq. 3): semantic support for the triphone centred on the word's stem vowel.

Equations

• Phenomena.Phonology.Studies.Saito2025.semSupVowel D s vowelTriphoneIdx = Theories.Processing.Lexical.Discriminative.semSup D s vowelTriphoneIdx

@[reducible, inline]

abbrev Phenomena.Phonology.Studies.Saito2025.semSupSuffix (D : GermanInflectionalDLM) (s : GermanWord2VecVec) (suffixTriphoneIdx : Fin TriphoneCount) : ℝ

SemSupSuffix (paper §3.1 eq. 4): semantic support for the triphone centred on the suffix exponent ([t] in this paper). The headline measure of paper §3.2.2: replacing the binary inflectional-status factor with semSupSuffix improves the tongue-position GAMM by 142.87 AIC units.

Equations

• Phenomena.Phonology.Studies.Saito2025.semSupSuffix D s suffixTriphoneIdx = Theories.Processing.Lexical.Discriminative.semSup D s suffixTriphoneIdx

theorem Phenomena.Phonology.Studies.Saito2025.saito_close_meanings_imply_close_form (D : GermanInflectionalDLM) (s₁ s₂ : GermanWord2VecVec) {ε : ℝ} (h : ‖s₁ - s₂‖ ≤ ε) : ‖D.production s₁ - D.production s₂‖ ≤ ‖LinearMap.toContinuousLinearMap D.production‖ * ε

Quantitative form of the DLM's articulation prediction. Paper §3.3 reports that the trained DLM's production map yields tongue-position predictions consistent with empirical measurements. The Lipschitz form: any GermanInflectionalDLM sends close-in-meaning word pairs to close-in-form triphone-vectors, with constant ‖production‖.

This is the third consumer of dlm_neighbor_centroids_imply_neighbor_contours (after Chuang 2026 and Lu 2026), validating that the polymorphic substrate accommodates German morpho-phonetics with no specialisation beyond carrier-type instantiation.

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.

Frequency × inflectional status interaction (paper §2.2.1, Table 1). For non-inflected words, higher (log) frequency predicts higher tongue- tip positions (articulatory reduction). For inflected words this reduction effect is significantly attenuated (interaction term te(Freq, Time):Inflected: edf=7.51, F=15.83, p<0.001). The same interaction is observed for tongue-body positions (paper §2.2.2, Table 2; F=3.29, p=0.020).

SemSupSuffix is the strongest predictor of inflectional status (paper §3.2.1, Fig. 10). In a Random Forest analysis with nine DLM-derived semantic measures as candidate predictors, SemSupSuffix ranks highest; SemSupVowel ranks second; SemSupWord ranks fourth (after PredAcc). Inflected words have significantly higher SemSupSuffix (Mann-Whitney U=152,201, p<0.001) and higher SemSupWord; lower SemSupVowel (paper §3.2.2, Fig. 11abc).

SemSupSuffix replaces InflStatus in the GAMM (paper §3.3, Table 3). Replacing the binary factor InflStatus with the continuous SemSupSuffix measure in the tongue-position GAMM reduces AIC by 142.87 units (62.64 ML score units), with one fewer effective degree of freedom. The DLM-derived continuous measure is structurally simpler than the categorical alternative and fits the data better.

Frequency interaction explained by SemSupSuffix (paper §3.4). The interaction te(Time, SemSupSuffix, Freq) (edf=20.31, F=30.92, p<0.001) shows that higher SemSupSuffix correlates with lowered tongue positions for high-frequency words (= articulatory enhancement), while low-SemSupSuffix high-frequency words show raising (= articulatory reduction). The frequency paradox dissolves: both effects coexist, modulated by semantic support.

Implications recorded in the paper's discussion

• No morphological-boundary primitive needed (paper §4): the apparent boundary effect is driven by inflectional semantics — SemSupSuffix reflects how well a word's meaning supports its word-final triphone, which is high for inflected words because inflectional meanings are tied to the suffix.
• Anti-WEAVER++ (paper §4 contra @cite{levelt-roelofs-meyer-1999}, Roelofs 1997): production models with intermediate symbolic morphological layers are not required; direct meaning ↔ form mappings via the DLM suffice.
• Reduction-enhancement composite (paper §4 conclusion): both effects can be expressed within the DLM as h_{ω,k} * Ĉ_{i,s} — informativity (h) modulates the strength of semantic support (Ĉ) on word-final triphones. (See @cite{gahl-baayen-2024} for an analogous formulation on word duration.)
• Cross-modal substrate validation: the paper's success applying DLM to articulatory (tongue-tip / tongue-body trajectories) rather than acoustic data demonstrates that the form ↔ meaning isomorphism finding of the Mandarin tone studies generalises beyond pitch — cf. Lu et al. 2026 §5 conjecture that "form-meaning isomorphism is not a tone-language quirk".