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.
Relational Summary
Four sentences. Each carrying one layer of the framework's architecture.
The terrain properties (slope, temperature, friction, slippery, tension, flexion, elevation) describe the local and global geometry of the loss surface — the fixed mathematical landscape training navigates, formally defined by L(θ) and its derivatives — while the macro-topology shapes (bowl, valley, saddle, plateau, ridge, basin) are the emergent large-scale features that terrain properties produce in aggregate, determining where models converge, stall, or drift.
The navigator properties (density, perplexity, probability, coupling, viscosity, elasticity, memory) are conjugate to terrain — not a second independent coordinate system but a description of the same system from its momentum axis — and the primary generative quantity at their interface is potential difference: the gap between navigator state and terrain geometry that creates the condition for movement; tension is what holds that potential difference stable without collapsing it; harmonics is the dynamic behavior that emerges when potential and tension interact over time; and resistance, laminar flow, and turbulent flow are derived vocabulary describing the observable character of movement once it is occurring, not a formal layer and not primary.
Structural integrity is a genuinely separate category governing whether the model's internal representational geometry holds under sustained inference load — context pressure, token accumulation, competing objective tension — a property invisible to both the static landscape description and training-time navigator properties, measurable through activation drift analysis across varying context conditions, and not fully reducible to viscosity, elasticity, and memory despite formal overlap at the boundary.
The archaeological signal Atlas seeks lives in the scar tissue of turbulent training — not merely high-resistance regions but places of unresolved potential difference, where the gap between navigator state and terrain geometry never closed, where tension never found its harmonic, where the system stayed charged without discharging, and where the geological record of that retained potential is preserved in the weight structure of a frozen model as high-perplexity, high-viscosity saddle and valley behavior readable not as active turbulence but as the stratigraphic evidence of where the landscape's charge was never released; this claim is asserted on the framework's internal logic and requires formal derivation and empirical testing to be established.