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Dupoux's Developmental Constraints and TEO Emergence

How developmental learning theory maps onto the TEO framework's constraint hierarchy.

Background: Dupoux's Insight

Emmanuel Dupoux's research program on early language acquisition demonstrates that human infants do not learn language from scratch. They exploit innate computational constraints — biases toward certain sound categories, statistical regularities, and social contingencies — that channel the learning process. Without these constraints, the combinatorial space of possible languages would be unlearnable from the available data.

The key insight: constraints are not obstacles to learning — they are prerequisites for it. A system with no constraints has too many degrees of freedom; a system with too many constraints cannot adapt. Developmental learning operates in the narrow band between.

Mapping to TEO: Three Constraint Regimes

The TEO framework instantiates three distinct constraint types that parallel Dupoux's developmental architecture:

System A — Bottom-Up Emergence (Replicator Dynamics)

\[\frac{dx_i}{dt} = x_i \left( f_i(\mathbf{x}) - \bar{\phi}(\mathbf{x}) \right)\]

This is unconstrained competition: agents grow or shrink based solely on relative fitness. No external structure is imposed. It corresponds to the infant's raw statistical exposure — frequency counting without phonemic categories.

Prediction: System A alone converges to winner-take-all dynamics. In developmental terms: without categorical constraints, the learner memorizes frequent patterns but fails to generalize (cf. grokking before the phase transition).

System B — Top-Down Regulation (Homeostatic Brake)

\[\mathcal{H}_i(\mathbf{x}) = -\gamma \cdot \max\left(0,\ x_i - x_{\text{crit}}\right)\]

This is imposed categorical structure: hard constraints that limit the space of permissible configurations. It corresponds to the innate biases Dupoux identifies — phonemic boundaries, prosodic templates, social contingency detectors — that constrain what the learner can represent.

Prediction: System B alone produces stable but rigid configurations. The system cannot adapt to novel environments because its constraints are fixed.

System M — Middle-Out Coupling (Kuramoto + Constraints)

The full TEO system, where bottom-up competition, top-down regulation, and lateral coupling (\(K\)-mediated synchronization) operate simultaneously:

\[\frac{dx_i}{dt} = x_i \left( f_i - \bar{\phi} \right) + \mathcal{H}_i\]
\[\frac{d\theta_i}{dt} = \omega_i + \frac{K}{N} \sum_j A_{ij} \sin(\theta_j - \theta_i)\]
\[\sum_i \eta_i x_i f_i \leq D_{\max}\]

This is constrained learning: the bottom-up dynamics provide the raw material, the top-down constraints provide the categorical scaffolding, and the lateral coupling provides the social-contextual modulation. This is the regime Dupoux's empirical work identifies as the actual developmental trajectory.

Prediction: System M outperforms both A and B because it combines flexibility (A) with structure (B) and social coupling.

Testable Predictions

  1. Constraint ordering matters. In the TEO civilization simulation, initializing with System A (unconstrained competition) then adding System B (homeostasis) produces different long-term attractors than initializing with both simultaneously. This parallels Dupoux's finding that the timing of constraint introduction affects learning outcomes.

  2. Constraint removal reveals developmental stage. Removing the homeostatic brake (\(\gamma \to 0\)) at different points in the TEO simulation should produce different collapse dynamics depending on how much structure has already been internalized. Early removal → immediate monopoly. Late removal → delayed collapse with transient stability. This mirrors the critical period hypothesis in language acquisition.

  3. The coupling strength \(K\) plays the role of social interaction. Below \(K_c\), the system cannot synchronize even with perfect constraints — corresponding to the finding that language acquisition requires social contingency, not just statistical exposure.