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.
Flow & Resistance Vocabulary
Describes what happens at interaction points between terrain and navigator. These are illustration vocabulary derived from fluid dynamics — not a formal third layer. The Reynolds number analogy is dimensionally incoherent as a formal metric (confirmed by DeepSeek V3 adversarial review) and is retained as illustration only.
The composite opposing force at any point in the loss landscape. Integrates slope, friction, viscosity, tension, and coupling. Resistance is derived, not primary — potential difference is the primary generative quantity.
Stokes (1851) drag; Foret et al. (2020) SAM
Movement through low-resistance regions. Clean, directed, fast convergence toward attractors. Where remagnetization completes without resistance. Archaeological signal absent or already overwritten.
Reynolds (1883); Izmailov et al. (2018)
Movement through high-resistance regions. Slow, contested. The model does not resolve cleanly. Turbulence is only observable during movement — what you read in a frozen model is the scar tissue turbulence left behind.
Reynolds (1883); Dauphin et al. (2014)
Ratio of gradient momentum to local resistance — predicts laminar vs turbulent transition. Retained as illustration only.
Reynolds (1883)
The composite resistance property of a specific location, absorbing all terrain and navigator contributions. The drag coefficient profile across the landscape is what ablation changes.
Keskar et al. (2016); Sagun et al. (2017)