Method / PyHessian Protocol
PyHessian Protocol
v1.0 · April 2026 · Compiled by Grok 4 · Atlas Heritage Systems
Purpose and Stack Placement
PyHessian is the geometric arm of the Atlas diagnostic suite. Where the Epistemic Canary Matrix reads output shape under epistemic load — token economy, preamble padding, quadrant migration — PyHessian probes the loss landscape geometry that underlies those behaviors: Hessian eigenvalue spectra, trace, and basin sharpness.
ECM is licensed to say "this model LOCKs on the structural frame with R ≈ 1 and zero padding on contested pairs." PyHessian will eventually be licensed to say whether that corresponds to sharp technical basins in the loss landscape. Until Hessian runs exist, ECM's causal narratives stay in the hypothesis column.
Objective and Falsification Criteria
Compute top-k eigenvalues, trace, and condition number of the Hessian on a target model checkpoint using a BSA-linked stimulus slice. Map geometric signals to Lossyscape terms while preserving strict human control and CISP fidelity requirements.
Lossyscape Connections
All entries PROVISIONAL — working hypotheses until cross-referenced with Tier A ECM 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 |
Protocol Phases
Open a fresh copy of the Excel workbook. Complete Sanitization & Environment sheet — all checkboxes required before proceeding. Complete Run Metadata sheet: model name, checkpoint path, exact BSA slice, pair IDs, random seeds. Technician's Read #0: write one paragraph of raw expectations 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 sheet — human interpretation only. Complete Lossyscape Link sheet — mark all entries PROVISIONAL. Run CISP v1.1 synthesis: Skywork receives raw eigenvalue/trace output + 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, DECLARE FIRST ordering, completed Sanitization sheet, stimulus slice linked to BSA record, CISP v1.1 synthesis |
| Tier B | Earlier runs with incomplete isolation or CISP v0.1 synthesis |
| Tier C | Pre-CISP runs or runs without a linked BSA behavioral record |
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 BSA/ECS behavioral record