Lu, Chuang and Baayen (2026): The realization of tones in spontaneous spoken Taiwan Mandarin

Lu, Chuang and Baayen survey the f0 contours of disyllabic words across the twenty tone patterns of Taiwan Mandarin in Fon's corpus of spontaneous speech, and find that word and sense outweigh tone pattern as predictors of the contour (§3.4). Following Chuang, Bell, Tseng and Baayen, they fit a linear map from 768-dimensional contextualized embeddings to 100-sample normalized pitch contours by least squares on the training tokens (§4.3), the method of Gahl and Baayen. The map sends the centroid embedding of each tone pattern to a contour close to the one a generalized additive model assigns the pattern (§4.4, Fig. 9).

The centroid of a tone pattern is a mean of means. The embeddings of each word type's tokens are averaged, and these word-type centroids are averaged in turn, so that every word type weighs equally (§4.4). Least squares fits the mean contour of every word type that is linearly decodable from the embeddings, and linearity carries the outer average, so the map sends the pattern's centroid embedding exactly to the same mean of means of its training contours.

The discussion (§5) answers the tone-sandhi objection on two grounds. T3-T3 and T2-T3 are neutralized in Taiwan Mandarin, as the authors' earlier study shows, and the model predicts forms from meanings, never forms from forms, so the tone-pattern contours emerge without the model being told the patterns. Xu's laboratory contours match the predicted ones for several patterns (Fig. 11).

Main statements

• LuChuangBaayen2026.production_centroid_centroid_eq_of_decodable: if every word type of a tone pattern is linearly decodable from the embeddings, the least-squares map sends the pattern's centroid embedding to the centroid of its word types' mean training contours.

Implementation notes

• A tone pattern is the set of its word types, and a word type the set of tokens carrying its label.
• Fig. 9 compares the predicted contours with those of the additive model, not with the averaged training contours, so the similarity the paper reports is approximate. The additive models and the nearest-neighbour accuracies are not represented.

References

• Y. Lu, Y.-Y. Chuang and R. H. Baayen, The realization of tones in spontaneous spoken Taiwan Mandarin: a corpus-based survey and theory-driven computational modeling (2026)
• Y. Lu, Y.-Y. Chuang and R. H. Baayen, Form and meaning co-determine the realization of tone in Taiwan Mandarin spontaneous speech (2024)
• Y.-Y. Chuang, M. J. Bell, Y.-H. Tseng and R. H. Baayen, Word-specific tonal realizations in Mandarin (2026)
• S. Gahl and R. H. Baayen, Time and thyme again (2024)
• J. Fon, A preliminary construction of Taiwan Southern Min spontaneous speech corpus (2004)
• Y. Xu, Contextual tonal variations in Mandarin (1997)

@[reducible, inline]

abbrev LuChuangBaayen2026.PitchSampleCount : ℕ

The paper samples 100 f0 values per token in normalized time, centered and scaled per token (§4.1).

Equations

• LuChuangBaayen2026.PitchSampleCount = 100

@[reducible, inline]

abbrev LuChuangBaayen2026.PitchVector : Type

A pitch contour at the paper's resolution.

Equations

• LuChuangBaayen2026.PitchVector = DiscriminativeLexicon.FormVec LuChuangBaayen2026.PitchSampleCount

@[reducible, inline]

abbrev LuChuangBaayen2026.TaiwanMandarinDLM : Type

The paper's DLM maps the 768-dimensional CKIP GPT-2 contextualized embeddings of [CBTB26] to 100-sample pitch vectors (§4.2).

Equations

• LuChuangBaayen2026.TaiwanMandarinDLM = DiscriminativeLexicon.Linear ℝ LuChuangBaayen2026.PitchVector ChuangEtAl2026.ContextualEmbedding

theorem LuChuangBaayen2026.production_centroid_centroid_eq_of_decodable {m : ℕ} {W : Type u_1} [DecidableEq W] {D : TaiwanMandarinDLM} {data : DiscriminativeLexicon.TrainingExperience m PitchSampleCount ChuangEtAl2026.CKIPGPT2HiddenDim} (hD : DiscriminativeLexicon.Linear.IsELTrainedOn data D) (word : Fin m → W) {T : Finset W} (hT : T.Nonempty) (hne : ∀ τ ∈ T, ∃ (i : Fin m), word i = τ) (hdec : ∀ τ ∈ T, ∃ (ℓ : ChuangEtAl2026.ContextualEmbedding →ₗ[ℝ] ℝ), ∀ (i : Fin m), ℓ (data.S i) = if word i = τ then 1 else 0) : D.production (Finset.centroid ℝ T fun (τ : W) => Finset.centroid ℝ {x : Fin m | word x = τ} data.S.row) = Finset.centroid ℝ T fun (τ : W) => Finset.centroid ℝ {x : Fin m | word x = τ} data.C.row

The centroid of a tone pattern averages the centroids of its word types T, each the mean over the tokens of the type (§4.4). If every word type of the pattern has a training token and is linearly decodable from the embeddings, a least-squares-trained production map sends the pattern's centroid embedding to the same average of its word types' mean target contours (Fig. 9).