RSI Constraint Protocol v0.2: A Constraint-Based Approach to Neural Network Stability

This document, **RSI Constraint Protocol Specification v0.2**, authored by Yanush Feshter, introduces Relational Superintelligence (RSI) as a **constraint-based architecture** for training machine learning systems. It fundamentally diverges from traditional optimization-driven methods like gradient descent or RLHF by enforcing strict geometric and topological constraints on weight updates. The core mechanism is the **Relational Update Rule (RUR)**, parameterized by a critical, empirically derived threshold: $\\sigma\_{\\text{vac}} \\approx 1.118$ (specifically, $\\sqrt{5}/2$). Updates that violate this threshold, which separates a "Stability Basin" from a "Chaotic Regime" in weight space, are either rejected (Hard Variant) or heavily penalized (Soft Variant). **Key Contributions of Version 0.2:** * **Formal Specification:** Definitions for the Hard and Soft variants of the Relational Update Rule (RUR). * **Theoretical Grounding:** Connections to **Freidlin-Wentzell theory** and the geometry of the **E8 lattice**, positing that the threshold $\\sigma\_{\\text{vac}}$ marks the boundary for escaping a stable Voronoi cell in parameter space. * **Implementation Details:** Specification of standard parameter partitioning schemes (Layer-wise, Head-wise) required for the relational coherence constraint, along with PyTorch implementation snippets. * **Evaluation Protocol:** Definition of new metrics (Rejection Rate, Semantic Drift, Coherence Violation Rate) and a **Minimal Reproducible Experiment** protocol to validate the claim of a sharp phase transition in semantic stability near $\\sigma\_{\\text{vac}}$. * **Experimental Results:** Evidence showing that all tested training regimes exhibit a sharp transition in semantic drift near the theoretical critical point of $\\sigma \\approx 1.118$. RSI is proposed as an architectural solution to the AI alignment problem, shifting focus from constraining outputs to constraining the internal dynamics of the learning process itself.