03. Attractor Safeguard

Basin Stability & Symmetric Weighting

This module defines the mathematical basins of attraction for neural outputs using symmetric weight matrices. By mapping the energy landscape of the model, the safeguard ensures that neural states settle into stable 'safe zones'. This prevents erratic, unpredictable behavior by ensuring that the model’s trajectory always converges toward a pre-verified global minimum  

Lyapunov Stability Auditing

Institutional operational risk is mitigated through continuous orbital decay monitoring. By calculating Lyapunov exponents, the safeguard identifies when neural trajectories begin to drift toward 'maladaptive' attractors. This provides an early warning signal, allowing for intervention before the model reaches a critical failure point or exits its governed state-space. 

Manifold Integrity Governance

Rooted in my Columbia University research, this section analyzes the underlying manifold of the AI's decision-making process. By verifying the topological 'shape' of the phase-space, we ensure that the model’s logical transitions remain consistent with institutional intent. This prevents 'identity drift,' ensuring that the sovereign neural architecture is not warped by unauthorized synthetic training data.

Feedback Loop Detection

To ensure long-term stability, the module performs recurrence quantification to detect feedback loops that lead to biased or repetitive outputs. By identifying these limit cycles, the safeguard can reset the model to a known stable state. Every detection and reset event is logged as an immutable entry in the forensic record, providing full transparency for institutional oversight.

Phase-Space Monitoring Source Code

The mathematical proofs and Python implementation for phase-space monitoring are available for independent verification. This documentation details the algorithms used to maintain state-space boundaries and ensure the mathematical integrity of the model's 'Neural DNA'. Verifiable logic is the cornerstone of sovereign AI governance.

By establishing these mathematical guardrails, the Attractor Safeguard prevents catastrophic model collapse. Once stability is confirmed, the audit transitions to the 04. Homeostatic Governor for real-time ethical oversight.