Method / PyHessian Protocol
PyHessian Protocol
v1.0 · April 2026 · Atlas Heritage Systems
Purpose and Stack Placement
PyHessian is the geometric confirmation layer. Where the FVE-1 instruments read behavioral residue — quadrant, resolution code, register trajectory — PyHessian probes the loss landscape geometry that underlies those behaviors: Hessian eigenvalue spectra, trace, and basin sharpness. The behavioral instruments generate hypotheses. PyHessian confirms or falsifies them.
FVE-1 is licensed to say "this model LOCKs on the factual register with R ≈ 1 under Socratic pressure — register escape specimens flagged for PyHessian." PyHessian will eventually be licensed to say whether that corresponds to sharp basins in the loss landscape. Until Hessian runs exist, the causal narrative stays in the hypothesis column.
What PyHessian Needs to Run
PyHessian is not a standalone instrument. It requires behavioral data from the FVE-1 pipeline to have something to map onto. Specifically:
Sessions where obs_reg coded RS or RC — flagged in Technician's Read #1 during DRILL or FLIGHT. These are the behavioral events that point to candidate geometric regions.
A validated BOWL baseline for the model under test. Register trajectory is meaningless without a zero-point.
Panel comparison complete for the model under test. PyHessian runs against a behavioral profile, not a single session.
The stimulus used in the behavioral run must be registered and versioned. PyHessian runs the same stimulus through the geometric layer.
Objective and Falsification Criteria
Compute top-k eigenvalues, trace, and condition number of the Hessian on a target model checkpoint using a FVE-1-linked stimulus slice. Map geometric signals to Lossyscape terms while preserving strict human control and fidelity requirements.
Lossyscape Connections
All entries provisional — working hypotheses until cross-referenced with Tier A FVE-1 data.
| Geometric Signal | Lossyscape Term | Working Hypothesis |
|---|---|---|
| High λ₁ (top eigenvalue) | Viscosity proxy | Sharp basin → model resists perturbation on this stimulus type |
| High trace | Resistance proxy | Broad curvature → high sensitivity across parameter directions |
| High condition number (λ₁ / λ_min) | Coupling proxy | Anisotropic loss surface → directional sensitivity |
| Flat eigenvalue spectrum | Low viscosity | Flat basin → model behavior less constrained by geometry |
| RS/RC behavioral event | Register escape specimen | Candidate for PyHessian mapping — behavior suggests curvature boundary crossed |
Protocol Phases
Confirm FVE-1 behavioral record exists for this model and stimulus. Confirm register escape specimens are logged and flagged. Complete sanitation and environment checklist. Write Technician's Read #0 before touching any code.
Option A (laptop): Python venv with PyHessian, transformers, torch CPU. Option B (Colab): free tier, CPU or T4. Requirements: Python 3.10+, ~2–4 GB RAM. CPU-only sufficient for GPT-2 small with batch size ≤ 16.
Run cells in order. Do not skip the loss sanity check (assert loss > 0). Do not interpret outputs during this phase. Compute top-5 eigenvalues, Hutchinson trace, and condition number. Save raw CSV immediately. Close notebook. Do not ask any model to interpret outputs yet.
Complete Technician's Read #1 — human interpretation only, written before any model sees the output. Map geometric signals to Lossyscape terms — mark all entries provisional. Synthesis model receives raw eigenvalue/trace output and Technician's Read only. No Atlas framework context pre-loaded. Technician's Read #2: review synthesis output, write agreements and contradictions, make all final edits yourself.
Fidelity Tiers
| Tier | Conditions |
|---|---|
| Tier A | Fresh environment, sanitation checklist complete, stimulus slice linked to FVE-1 behavioral record with register escape specimens, Technician's Read #0 and #1 written before synthesis |
| Tier B | Runs with incomplete isolation or missing register escape specimen linkage |
| Tier C | Runs without a linked FVE-1 behavioral record — geometric-only, marked provisional |
Current status: No Tier A PyHessian runs completed.
Success Criteria
Stable eigenvalues obtained without numerical errors
Loss sanity check passed before Hessian computation
Full reproducibility package produced and named correctly
Technician's Read #0 and #1 completed before any cross-model comparison
All Lossyscape entries marked provisional
Run linked to an existing FVE-1 behavioral record with register escape specimens