Methods; SI: numerical instrument

Numerical and solver checks

The paper reports dense/operator comparisons, iterative-solver checks and precision controls for the metric computations used by its experiments.

Checking the reduced solve against a dense solve

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Precision and larger-model controls

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Methods and interpretation

The checks cover the solver tolerances, numerical precision and reference metrics used in the experiments.

Procedure in the paper: Reproduce the stated dense-versus-operator fixtures, precision settings and solver residual checks at the declared problem sizes. Validate affected numerical endpoints against the corresponding reference calculations.

Code and data

Woodbury and dense solver comparisonZIP

v0.1.0 · 52 KB · View source on GitHub ↗

The fixed float64 synthetic Woodbury-versus-dense solver identity check; no model or dictionary training.

Precision and large-model controlsZIP

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.