Figure 2b; Extended Data 1a
Local behavioural cost
The quadratic KL prediction matches 99 resolved local measurements across 11 models, with median measured-to-predicted ratio 1.000.
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Methods and interpretation
Quarter-, half- and three-quarter-depth injections. The comparison uses the coarsest numerically resolved small steps.
Procedure in the paper: Load the fixed model snapshots and contexts, compute the pullback Fisher operator, apply the specified small perturbations and measure numerically stable KL. Repeat the reference-transport coordinate check.
Local prediction
99 calibrated cells at the coarsest resolved local step for each cell. The diagonal denotes exact agreement.
A token is a possible next piece of text. KL divergence compares the complete distribution of next-token probabilities; nats are its units.
Code and data
v0.1.0 · 70 KB · View source on GitHub ↗
The 99-cell native-model quadratic KL calibration with the fixed floor extension, plus the 12-prompt Pythia-410M coordinate-covariant regularization audit.
v0.1.0 · 60 KB · View source on GitHub ↗
The float32/bfloat16 direction comparison, nine retained 6.9B calibration measurements and late-layer solver/steering diagnostics.
Each standalone package includes code, shared helpers, required small inputs and reference results, with setup and commands in its README. Model weights and public datasets are obtained separately where needed.
Download complete source (v0.1.0) for all experiments and the companion website.