Discriminative Lexicon Model — linear substrate

The Discriminative Lexicon Model (DLM) is a theory of lexical processing in which form and meaning are related by learned mappings between vector spaces rather than by an inventory of stored, decomposed form–meaning entries ([baayen-2019]). At the endstate of learning the model is a pair of linear maps — the papers' comprehension matrix F (Ŝ = CF) and production matrix G (Ĉ = SG) — fitted by linear discriminative learning, the least-squares estimation of [heitmeier-chuang-baayen-2026]. The two maps are the model's entire "lexicon". The kernel of the production map is the DLM's neutralization locus: two meanings surface as identical forms iff their difference lies in LinearMap.ker D.production (LinearMap.sub_mem_ker_iff).

The deep replacements for the linear maps — ResLDL ([chuang-bell-tseng-baayen-2026]) and DDL ([heitmeier-schmidt-lensch-baayen-2025]) — are not formalised.

Main declarations

• Linear R F M: a pair of linear maps between form and meaning carriers.
• FormVec, MeaningVec: Fin n → ℝ carriers for the studies' specialisations.

References

• [R. H. Baayen, Y.-Y. Chuang, E. Shafaei-Bajestan and J. P. Blevins, The discriminative lexicon (2019)][baayen-2019]
• [M. Heitmeier, Y.-Y. Chuang and R. H. Baayen, The Discriminative Lexicon (2026)][heitmeier-chuang-baayen-2026]
• [Y.-Y. Chuang, M. J. Bell, Y.-H. Tseng and R. H. Baayen, Word-specific tonal realizations in Mandarin (2026)][chuang-bell-tseng-baayen-2026]
• [M. Heitmeier, V. Schmidt, H. P. A. Lensch and R. H. Baayen, Is deeper always better? (2025)][heitmeier-schmidt-lensch-baayen-2025]

structure DiscriminativeLexicon.Linear (R : Type u_1) (F : Type u_2) (M : Type u_3) [Semiring R] [AddCommMonoid F] [AddCommMonoid M] [Module R F] [Module R M] : Type (max u_2 u_3)

The endstate of a Discriminative Lexicon Model with linear mappings: a comprehension map and a production map between form and meaning carriers, fitted by linear discriminative learning ([heitmeier-chuang-baayen-2026]).

• comprehension : F →ₗ[R] M

  The form → meaning map — the papers' comprehension matrix F (Ŝ = CF).

• production : M →ₗ[R] F

  The meaning → form map — the papers' production matrix G (Ĉ = SG).

@[reducible, inline]

abbrev DiscriminativeLexicon.FormVec (formDim : ℕ) : Type

A formDim-dimensional form vector over ℝ.

Equations

• DiscriminativeLexicon.FormVec formDim = (Fin formDim → ℝ)

@[reducible, inline]

abbrev DiscriminativeLexicon.MeaningVec (meaningDim : ℕ) : Type

A meaningDim-dimensional meaning vector over ℝ.

Equations

• DiscriminativeLexicon.MeaningVec meaningDim = (Fin meaningDim → ℝ)