What question did this study set out to answer?

The aim is to explore how cognitive systems achieve optimal performance at a specific level of misalignment.

April 8, 2026Open Access

Optimization-Induced Dynamics and the Inverted-U: A Distillation-Based Theory of Optimal Misalignment

Key Points

The aim is to explore how cognitive systems achieve optimal performance at a specific level of misalignment.
Developed 'Ma Theory' to describe optimal misalignment.
Used stochastic gradient descent (SGD)-driven distillation for optimization.
Conducted experiments with Pythia-410m and Pythia-160m models.
Analyzed the relationship between structural divergence and emergent utility.
Found an inverted-U relationship indicating optimal misalignment.
Results showed statistical significance with p=0.0007.
Confirmed that utility is maximized at a specific degree of structural divergence.

Abstract

Ma Theory proposes that perfect agreement between cognitive systems is not optimal. Instead, emergent utility is maximized at an optimal degree of structural divergence (ε*), forming an inverted-U relationship. This phenomenon appears only under optimization-induced dynamics (SGD-driven distillation), not under linear weight interpolation. Experiments on Pythia-410m and Pythia-160m confirm the inverted-U with statistical significance (p=0.0007).

Optimization-Induced Dynamics and the Inverted-U: A Distillation-Based Theory of Optimal Misalignment

Key Points

Abstract

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