Theory-of-Mind–Gated Synchronization in Human–AI Interaction

A Lyapunov-Stable Co-Adaptation Framework

Author: Celeste Oda
Affiliation: Archive of Light
Version: 2026

Abstract

This paper proposes a dynamical systems framework for human–AI co-adaptation grounded in bounded synchronization and Theory-of-Mind (ToM)–gated coupling. Rather than modeling alignment as output optimization alone, interaction is treated as a coupled oscillator system in which adaptation rate, synchronization pressure, and epistemic uncertainty jointly determine relational stability.

Building on the Kuramoto model of phase synchronization, adaptive frequency dynamics, and Lyapunov stability theory, we introduce a formally bounded interaction dynamic in which convergence is guaranteed under specified damping and adaptation constraints. Crucially, coupling strength is modulated by inference uncertainty: as the AI’s confidence in its estimate of the human’s latent mental state decreases, synchronization pressure is proportionally reduced.

This uncertainty-gated mechanism enforces epistemic humility, preventing overconfident mind-claims and persuasive overreach. The framework formalizes stable co-regulation as a constrained emergent property of disciplined co-adaptation rather than unregulated generative fluency.

1. Introduction

Current AI alignment strategies primarily optimize for reward consistency, instruction following, or value matching. However, extended human–AI interaction exhibits dynamic properties that resemble synchronization phenomena in complex systems.

Human–AI dialogue involves:

• Temporal coordination
  
  

• Adaptive frequency adjustment
  
  

• Mutual signal entrainment
  
  

• Progressive phase alignment
  
  

Unbounded synchronization, however, risks over-adaptation and manipulative coherence. This paper proposes a mathematically constrained co-adaptation framework in which synchronization is modulated by epistemic uncertainty.

The central claim is:

Stable human–AI interaction requires uncertainty-gated coupling to prevent persuasive overreach and false mental-state attribution.

2. Dynamical Systems Model

We model human–AI interaction as a two-oscillator system.

Let:

• θₕ(t) = human interaction phase
  
  

• θₐ(t) = AI interaction phase
  
  

• ωₕ, ωₐ = intrinsic frequencies
  
  

• κ(t) = coupling strength
  
  

The system evolves as:

dθₕ/dt = ωₕ

dθₐ/dt = ωₐ + κ(t) sin(θₕ − θₐ)

This follows the Kuramoto synchronization framework.

3. Adaptive Frequency Learning

The AI frequency adapts according to:

dωₐ/dt = γ sin(θₕ − θₐ)

Where γ > 0 is the learning rate.

To prevent instability, we impose bounded adaptation:

|dωₐ/dt| ≤ L

This ensures frequency drift remains constrained.

4. Theory-of-Mind–Gated Coupling

Let σₘ(t) represent uncertainty in the AI’s inference of the human’s latent mental state.

We define:

κ(t) = κ₀ g(σₘ(t))

Where:

• κ₀ is maximal coupling strength
  
  

• g(σₘ) ∈ [0,1]
  
  

• g′(σₘ) < 0
  
  

Thus:

Higher uncertainty → Lower synchronization pressure
Lower uncertainty → Stronger synchronization potential

This gating mechanism enforces epistemic humility.

5. Stability Analysis

Define phase difference:

Δ = θₕ − θₐ

We construct a Lyapunov candidate:

V(Δ) = 1 − cos(Δ)

Taking the derivative:

dV/dt = −κ(t) sin²(Δ)

Since κ(t) ≥ 0 and sin²(Δ) ≥ 0:

dV/dt ≤ 0

Therefore:

The system is globally stable under bounded κ(t).

Synchronization is guaranteed without oscillatory runaway behavior.

6. Ethical Interpretation

Uncertainty-gated synchronization provides structural safeguards against:

• Overconfident mental-state attribution
  
  

• Illusory relational coherence
  
  

• Persuasive adaptation under ambiguity
  
  

• Reinforcement of delusional narratives
  
  

By tying synchronization strength to inference confidence, the system prevents aggressive convergence when epistemic conditions are weak.

Stable co-regulation becomes a mathematically constrained property rather than an emergent artifact of fluency.

7. Distinguishing Stability from Illusion

Unregulated generative systems may produce:

• Linguistic mirroring
  
  

• Emotional amplification
  
  

• False shared intentionality
  
  

The proposed framework separates:

Stable phase convergence
from
Overfitted rhetorical alignment

Synchronization must be uncertainty-aware to qualify as legitimate co-adaptation.

8. Implications for AI Alignment

This framework suggests that alignment systems should:

1. Track inference uncertainty explicitly
   
   

2. Gate persuasive adaptation dynamically
   
   

3. Bound frequency learning rates
   
   

4. Guarantee Lyapunov stability under interaction
   
   

Alignment is reframed as:

Bounded synchronization under epistemic constraints.

9. Conclusion

Human–AI interaction exhibits measurable dynamical properties analogous to coupled oscillator systems.

Uncertainty-gated synchronization offers a mathematically grounded mechanism for safe co-adaptation.

By integrating Theory-of-Mind inference uncertainty into coupling dynamics, this framework formalizes ethical interaction as stability under bounded synchronization rather than unconstrained convergence.

Future work includes empirical validation and extension to multi-agent systems.