Study 3: Morpheme Order Optimization (Japanese & Sesotho)

[Byb85] [Dem92] [DM67] [HDF21] [KIKY13]

[HDF21] Study 3: morpheme orders in Japanese verb suffixes and Sesotho verb affixes are near-optimally efficient in terms of memory-surprisal trade-offs. The real morpheme orders achieve lower AUC than random baselines.

Japanese Verb Suffixes (SI §4.1, Table 2)

Seven suffix slots ordered from stem outward:

1. Derivation: -su (suru)
2. VALENCE: causative -(s)ase
3. VOICE: passive/potential -are, -rare
4. MOOD: desiderative -ta, politeness -mas
5. NEGATION: -na
6. TENSE/ASPECT/MOOD: -ta (past), -yoo (future)
7. Nonfinite: -te

Real order AUC ≈ 47.0 (morpheme level), baselines ≈ 47.2 (SI Figure 6).

Sesotho Verb Affixes (SI §4.2)

Prefixes: subject agreement, negation, tense/aspect, object agreement Suffixes: reversive, causative, neuter, applicative, completive, reciprocal, passive, tense, mood, interrogative/relative

Real order AUC ≈ 38.7 (morpheme level), baselines ≈ 38.8 (SI Figure 8).

[Byb85] Relevance Hierarchy

stem < valence < voice < aspect < tense < mood < agreement

Both Japanese suffixes and Sesotho suffixes respect this hierarchy: morphemes closer to the stem are more semantically relevant to the verb.

Data Source

https://github.com/m-hahn/memory-surprisal. Morpheme order data from SI §4.1-4.2, AUC values from SI Figures 6 and 8.

def Morphology.AffixTemplate.suffixRespectsRelevance (t : AffixTemplate MorphCategory) : Prop

The template's suffix order respects [Byb85]'s relevance hierarchy. Study-local: this study's two templates are its only consumers (descended from the substrate at the ≥2-consumer bar).

Equations

• t.suffixRespectsRelevance = Morphology.RespectsRelevanceHierarchy t.suffixSlots

@[instance_reducible]

instance HahnDegenFutrell2021.instDecidableSuffixRespectsRelevance (t : Morphology.AffixTemplate Morphology.MorphCategory) : Decidable t.suffixRespectsRelevance

Equations

• HahnDegenFutrell2021.instDecidableSuffixRespectsRelevance t = HahnDegenFutrell2021.instDecidableSuffixRespectsRelevance._aux_1 t

Japanese verb suffixes

SI §4.1's Japanese suffix order ([KIKY13], UD segmentation) is the language's affix template, so it lives as Fragment data in Fragments/Japanese/Morph.lean (Japanese.verbAffixTemplate); here we derive the slot list from it rather than re-typing it.

def HahnDegenFutrell2021.japaneseSuffixSlots : List Morphology.MorphCategory

Japanese suffix slots from stem outward, derived from the Fragment template Japanese.verbAffixTemplate (SI §4.1, [KIKY13]).

Equations

• HahnDegenFutrell2021.japaneseSuffixSlots = Japanese.verbAffixTemplate.suffixSlots

theorem HahnDegenFutrell2021.japanese_partial_bybee : have slots := [Morphology.MorphCategory.derivation, Morphology.MorphCategory.valence, Morphology.MorphCategory.voice, Morphology.MorphCategory.mood]; Morphology.RespectsRelevanceHierarchy slots

Japanese suffix order respects Bybee's hierarchy through the mood slot: derivation < valence < voice < mood. Beyond mood the order breaks — politeness (agreement), negation, then tense — so only this stem-adjacent prefix is checked; the full-order violation is japanese_violates_surveyed_relevance.

theorem HahnDegenFutrell2021.japanese_violates_surveyed_relevance : Bybee1985.SurveyedCloser Bybee1985.BybeeCategory.tense Bybee1985.BybeeCategory.mood ∧ ¬Japanese.verbAffixTemplate.suffixRespectsRelevance

Structural divergence from the survey. Bybee's Ch 2 §6 data ranks tense more stem-relevant than mood (Bybee1985.SurveyedCloser .tense .mood, which by Bybee1985.survey_order_iso_relevance is the substrate relevance order on these categories), yet Japanese's causative/desiderative layering places mood closer to the stem than tense (slots 4 vs 7) — so its full suffix order is not sorted by the relevance hierarchy. A genuine cross-linguistic counterexample to the §6 morpheme-order corollary, stated as a failure of the substrate predicate, not a positional count.

Sesotho verb affixes

SI §4.2's Sesotho affix order ([Dem92], [DM67]) lives as Fragment data in Fragments/Sesotho/Morph.lean (Sesotho.verbAffixTemplate); the slot lists below are derived from it.

def HahnDegenFutrell2021.sesothoSuffixSlots : List Morphology.MorphCategory

Sesotho suffix template, stem-outward, from the Fragment Sesotho.verbAffixTemplate (SI §4.2).

Equations

• HahnDegenFutrell2021.sesothoSuffixSlots = Sesotho.verbAffixTemplate.suffixSlots

def HahnDegenFutrell2021.sesothoPrefixSlots : List Morphology.MorphCategory

Sesotho prefix template, word-edge inward, from the Fragment Sesotho.verbAffixTemplate.

Equations

• HahnDegenFutrell2021.sesothoPrefixSlots = Sesotho.verbAffixTemplate.prefixSlots

theorem HahnDegenFutrell2021.sesotho_suffixes_respect_bybee : Sesotho.verbAffixTemplate.suffixRespectsRelevance

Sesotho suffixes respect the relevance hierarchy (valence < voice < tense < mood < nonfinite) — sorted by the substrate relevance order, which on the surveyed categories is Bybee's §6 order (Bybee1985.survey_order_iso_relevance). Contrast japanese_violates_surveyed_relevance: same surveyed order, opposite outcome.

Trade-off curves

Approximate AUC values from SI Figures 6 and 8. AUC is computed over the memory-surprisal trade-off curve (lower = more efficient). Values are multiplied by 100 for integer arithmetic.

def HahnDegenFutrell2021.japaneseRealAUC100 : ℕ

Japanese morpheme-level AUC × 100. Real ≈ 47.0, Random ≈ 47.2.

Equations

• HahnDegenFutrell2021.japaneseRealAUC100 = 4700

def HahnDegenFutrell2021.japaneseRandomAUC100 : ℕ

Equations

• HahnDegenFutrell2021.japaneseRandomAUC100 = 4720

def HahnDegenFutrell2021.sesothoRealAUC100 : ℕ

Sesotho morpheme-level AUC × 100. Real ≈ 38.7, Random ≈ 38.8.

Equations

• HahnDegenFutrell2021.sesothoRealAUC100 = 3870

def HahnDegenFutrell2021.sesothoRandomAUC100 : ℕ

Equations

• HahnDegenFutrell2021.sesothoRandomAUC100 = 3880

theorem HahnDegenFutrell2021.japanese_morpheme_efficient : japaneseRealAUC100 < japaneseRandomAUC100

Japanese real morpheme order is more efficient than random baselines.

theorem HahnDegenFutrell2021.sesotho_morpheme_efficient : sesothoRealAUC100 < sesothoRandomAUC100

Sesotho real morpheme order is more efficient than random baselines.

Prediction accuracy

From SI Figure 7 (Japanese) and Figure 9 (Sesotho). The optimized morpheme order achieves higher pairwise prediction accuracy than random baselines, and similar accuracy to the real order.

Values are accuracy × 1000.

def HahnDegenFutrell2021.japanesePairsOptimized : ℕ

Japanese morpheme prediction: optimized pairs accuracy × 1000.

Equations

• HahnDegenFutrell2021.japanesePairsOptimized = 953

def HahnDegenFutrell2021.japanesePairsRandom : ℕ

Japanese morpheme prediction: random baseline pairs accuracy × 1000.

Equations

• HahnDegenFutrell2021.japanesePairsRandom = 496

def HahnDegenFutrell2021.japanesePairsReal : ℕ

Japanese morpheme prediction: real order pairs accuracy × 1000.

Equations

• HahnDegenFutrell2021.japanesePairsReal = 953

theorem HahnDegenFutrell2021.japanese_optimized_beats_random : japanesePairsOptimized > japanesePairsRandom

Optimized and real orders vastly outperform random baseline for Japanese.

theorem HahnDegenFutrell2021.japanese_real_matches_optimized : japanesePairsReal = japanesePairsOptimized

The real Japanese order achieves accuracy matching the optimized order.

Bridge: Japanese causative is innermost suffix

The Bybee hierarchy predicts valence morphemes should be closest to the stem. Japanese -(s)ase (causative = valence) is slot 2, the first functional suffix after derivation. This is consistent with both:

1. The relevance hierarchy (valence is closest to stem meaning)
2. The memory-surprisal explanation (valence affects subcategorization, so placing it near the stem concentrates predictive information locally)

theorem HahnDegenFutrell2021.japanese_causative_is_valence : japaneseSuffixSlots[1]? = some Morphology.MorphCategory.valence

Japanese causative -(s)ase is in the valence slot (slot 2).

theorem HahnDegenFutrell2021.valence_is_innermost_functional : japaneseSuffixSlots[0]? = some Morphology.MorphCategory.derivation ∧ japaneseSuffixSlots[1]? = some Morphology.MorphCategory.valence

The valence slot is the first functional slot (after derivation).

Bridge: Japanese -(s)ase = Song's COMPACT morphological causative

Japanese -(s)ase is classified as a morphological COMPACT causative in [Son96]. The ik_ase entry in Fragments/Japanese/Predicates confirms this: causative = some.make.

theorem HahnDegenFutrell2021.ik_ase_is_causative : Japanese.Predicates.ik_ase.causative.isSome = true

The Japanese -(s)ase causative entry is causative (derived from causative).

theorem HahnDegenFutrell2021.ik_ase_is_make : Japanese.Predicates.ik_ase.causative = some Causative.make

Japanese -(s)ase uses the.make causative builder (direct causation).

Bridge: Relevance hierarchy ↔ Information locality

The Bybee hierarchy orders morphemes by semantic relevance to the stem. The memory-surprisal framework predicts that information-locality-optimal orderings place highly predictive morphemes close to the stem. These two predictions converge: semantic relevance correlates with predictive information, so the relevance hierarchy is an instantiation of information locality at the morpheme level.

The near-optimality of Japanese and Sesotho morpheme orders (japanese_morpheme_efficient, sesotho_morpheme_efficient) shows that real morpheme orders are close to the information-locality optimum, and the fact that they respect the relevance hierarchy (japanese_partial_bybee, sesotho_suffixes_respect_bybee) shows that the relevance hierarchy captures the right notion of locality.

theorem HahnDegenFutrell2021.relevance_hierarchy_implies_locality : Sesotho.verbAffixTemplate.suffixRespectsRelevance ∧ sesothoRealAUC100 < sesothoRandomAUC100