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Phase 0 Complete — Negative Result. HITL performed ~2× worse than baseline. Full post-mortem with root cause decomposition, corrected architecture, and Phase 1 pivot: ‣
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Canonical cluster anchors (previewable). Yennefer cluster · TAEX · Retraining loop · §6.17 · Integrations registry · Integrative Flow.
‣ · ‣ · ‣ · ‣ · ‣ · TAEX Intent Router — Agent-Based Routing with Dissonance Memory MCP · ‣ · ‣ · ‣
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Architecture Summary
Protocol: Ouroboros V2 — Spatial-RLHF for Non-Convex Optimization
Phase: 0 (Software-in-the-Loop)
Objective: Prove that a simulated human spatial heuristic, operating on a PCA-reduced 3D projection of a trapped optimizer's local loss landscape with Barnes-Hut repulsion encoding, produces a reverse-projected perturbation that escapes saddle points faster than isotropic random noise.
Pipeline
- Trap Detection — SGD stalls when $\|\nabla L\| < \epsilon$ and the Hessian has negative eigenvalues (saddle signature).
- Local Neighborhood Sampling — Sample $k$ points in $\mathbb{R}^n$ around the trapped state $theta^*$.
- PCA Projection — $P: \mathbb{R}^n \to \mathbb{R}^3$ via top-3 principal components of the sampled neighborhood.
- Barnes-Hut Repulsion Encoding — Each 3D sample point is assigned repulsion mass $m_i = L(theta_i) cdot |lambda_{text{neg}}(H_i)|$. Aggregate repulsion force on the trapped point computed via $O(N \log N)$ octree approximation.
- Simulated Human Agent — Computes escape vector $v_{3D}$ as the negative of the net repulsion force (path of least resistance).
- Reverse Projection — $\Delta\theta_n = P^+ \cdot v_{3D}$ via Moore-Penrose pseudo-inverse.
- Heuristic Injection — Perturb $theta^ leftarrow theta^ + alpha cdot Deltatheta_n$, resume SGD.
- Benchmark — Compare Time-to-Convergence (TtC) against random Langevin noise baseline.
Key Mathematical Grounding
- Saddle point detection: Eigenvalue decomposition of the Hessian $H$. Negative eigenvalues confirm saddle geometry (Dauphin et al., 2014).
- PCA pseudo-inverse: $P^+ = V_3 \in \mathbb{R}^{n \times 3}$ where $V_3$ are the top-3 right singular vectors. The reverse projection $\Delta\theta_n = V_3 \cdot v_{3D}$ is exact along the captured variance subspace.