Documentation

Studies.Saito2025

Saito, Tomaschek & Baayen (2025): Interaction of Frequency and Inflectional Status #

This file formalizes the paper's discriminative-lexicon account of a frequency effect that reverses with inflectional status. In tongue-position data from the Karl Eberhards Corpus of spontaneous southern German, high-frequency non-inflected words show articulatory reduction of the stem vowel while high-frequency inflected words do not, and the paper replaces the binary inflectional-status predictor by the semantic support that a word's meaning lends to its suffix triphone in a trained discriminative lexicon, which improves the tongue-position model with one fewer degree of freedom. The model is the substrate's linear discriminative lexicon over the paper's triphone form vectors and word2vec meaning vectors (GermanInflectionalDLM); close meanings yield close predicted articulations (close_meanings_imply_close_form), and when the suffix triphone is linearly decodable from meanings, training alone gives inflected words strictly greater suffix support than non-inflected ones, the direction of the paper's contrast (production_suffix_lt). The result bears on production models with a morpheme layer such as WEAVER++ ([LRM99], [Roe97]), since the apparent morphological-boundary effect is carried by inflectional semantics.

Implementation notes #

The paper's positional measures, the semantic support for the vowel and suffix triphones, are the predicted form D.production s at the two triphone indices, the substrate's semanticSupport at a coordinate indicator; the paper's triphone indexing is not reproduced. Its production matrix, solving SG = C, is the substrate's production, and its comprehension matrix, solving CF = S, is comprehension. The generalized additive models of the articulatory study are not formalized.

References #

source
@[reducible, inline]
abbrev Saito2025.TriphoneCount :
ℕ

The paper's CELEX-derived form matrix has TriphoneCount triphones.

Equations
Instances For
    source
    @[reducible, inline]
    abbrev Saito2025.Word2VecGermanDim :
    ℕ

    The pretrained German word2vec embeddings of [Mul15] have Word2VecGermanDim dimensions.

    Equations
    Instances For
      source
      @[reducible, inline]
      abbrev Saito2025.TriphoneVec :
      Type

      A triphone vector is a form vector over the paper's triphones; that its entries are zero or one is a property of the training data, not of the type.

      Equations
      Instances For
        source
        @[reducible, inline]
        abbrev Saito2025.GermanWord2VecVec :
        Type

        A German word2vec vector is a meaning vector of the embeddings' dimension.

        Equations
        Instances For
          source
          @[reducible, inline]
          abbrev Saito2025.GermanInflectionalDLM :
          Type

          The paper's discriminative lexicon is the linear model over German triphone form vectors and word2vec meaning vectors.

          Equations
          Instances For
            source
            theorem Saito2025.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

            Close meanings yield close predicted articulations, with the production map's norm as the constant.

            source
            theorem Saito2025.production_suffix_lt {m : ℕ} {D : GermanInflectionalDLM} {data : DiscriminativeLexicon.TrainingExperience m TriphoneCount Word2VecGermanDim} {q : DiscriminativeLexicon.FrequencyVector m} (hD : DiscriminativeLexicon.Linear.IsTrainedOn data q D) (hq : ∀ (i : Fin m), 0 < q i) {suffixIdx : Fin TriphoneCount} {w : GermanWord2VecVec →ₗ[ℝ] ℝ} (hw : ∀ (i : Fin m), w (data.S i) = data.C i suffixIdx) {i k : Fin m} (hik : data.C i suffixIdx < data.C k suffixIdx) :
            D.production (data.S i) suffixIdx < D.production (data.S k) suffixIdx

            When the suffix-triphone coordinate is linearly decodable from word meanings, the inflectional semantics the paper ties to the suffix, a trained lexicon's SemSupSuffix reproduces it exactly, so a word carrying the suffix triphone gets strictly greater suffix support than one lacking it, which is the direction of the paper's contrast between inflected and non-inflected words, obtained from the linear architecture alone.