Weak curvature dependence of interior steering precision

Determine whether a weak monotone dependence of interior steering precision on entropy-landscape curvature exists across regularized self-play games.

Background

The paper tests whether entropy-landscape curvature predicts steering precision across five games. The data show no detectable curvature-only dependence for interior targets, while curvature appears to predict where boundary saturation occurs.

However, the analysis uses only five games and therefore has sufficient power only against strong monotone relationships. The authors explicitly state that a weaker interior curvature law remains unresolved.

References

With $n=5$ games these tests have power only against strong monotone laws, so a weak interior law cannot be ruled out at this sample size.

— Steering Equilibrium Selection in Regularized Self-Play via the Reference Policy  (2609.19820 - Leal, 17 Sep 2026) in Section 4.6, “Curvature: $\kappa$ predicts boundary saturation, not interior precision”