Framework
Loss Landscape Vocabulary Framework
v13 · April 2026 · Atlas Heritage Systems · Working document — not a finished product
A note before the math
You don't need to understand any of this to read the Framework. But if you want to know why the Framework is built the way it is, the math is where the answer lives.
When a language model trains, it moves through a mathematical landscape — hills, valleys, flat plains — searching for the lowest point. The vocabulary on this page describes the features of that terrain: what makes one region harder to cross than another, what gets preserved in the difficult parts, and what gets smoothed away in the easy ones.
The archaeological claim Atlas makes is simple: the hard parts leave marks. Those marks are readable. That's what the instruments are built to find.
Start with the plain language description of each term. Follow the math when you need it.
How it all fits together
The Framework names the terrain. The instruments measure behavior on it. The schema defines how measurements get recorded. The protocols govern how they're taken — CISP is the governance layer that sits above every active instrument run, enforcing isolation, sequencing, and the human-judgment boundary.
Below the protocols, the automation layer handles transcription: parsing raw model output, computing what can be computed, and leaving blank what requires a Technician's call. Below that is the data the instruments produce over time — the actual record Atlas is building.
The geometry sits at the end of the chain. PyHessian doesn't measure behavior; it measures the mathematical terrain the Framework describes. When there's enough data, the Hessian eigenvalue analysis will either confirm the Framework's terrain claims or force a revision. Working hypotheses stay hypotheses until the math has something to argue with.
Architectural Structure of the Framework
How the layers relate to each other — resolved through adversarial review by GPT-4, GPT-5.2, Perplexity Sonar, DeepSeek V3, DeepSeek V3.2, Mistral Large, Mistral Large-3, Llama, Llama3.3 70B, Grok, Skywork, and Nemotron-3-Super-120B.
Position in parameter space. L(θ) and its derivatives. Readable only when model is stationary.
Momentum through parameter space. Observable only during movement. Viscosity, memory, perplexity.
- Basin connectivity — B(θA,θB) = min_φ max_t L(φ(t)) − max(L(θA),L(θB)) — not described by any qualifier. All seven are locally defined at a point.
- Symmetry orbits — permutation symmetry group |G| ≥ ∏ nₗ! · 2^nₗ — all seven qualifiers constant across this orbit. Ablation drift vector particularly damaged.
- Phase transitions — grokking demonstrates catastrophic behavioral change while loss surface remains smooth. Framework describes weight-space geometry, not representational geometry.