Hahn, Degen & Futrell 2021: memory-surprisal trade-off

[HDF21]

The Efficient Trade-off Hypothesis: natural word orders optimize the trade-off between memory investment and surprisal. Study 2 measures 54 Universal Dependencies languages against grammar-preserving random baselines: 50 have significantly more efficient trade-offs, and the four exceptions (Latvian, North Sami, Polish, Slovak) all have high branching direction entropy — word-order freedom correlates negatively with optimization strength (Spearman ρ ≈ −.58). Those measured results live in the paper and its data release, not here; the trade-off theory itself (the marginal-rate theorem and information locality) is formalized in Processing/Memory/SurprisalTradeoff.lean.

This file holds the study's structural argument as a stimulus contrast: information locality generalizes dependency length minimization, and consistent head direction yields strictly shorter dependencies than mixed direction on the same chain — the mechanism behind the low-entropy-implies-efficient half of the paper's Figure 13 pattern.

theorem HahnDegenFutrell2021.harmonic_dlm_holds : HahnDegenFutrell2021.harmonicChain✝.totalLength < HahnDegenFutrell2021.disharmonicChain✝.totalLength

Consistent head direction gives strictly shorter total dependency length than mixed direction on the same chain.