Figure 5c,d
Probability and read-out contributions
On the matched battery, probability-only is stronger for effective dimension, while the weighted profile is stronger for spectral shape.
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Methods and interpretation
Fourteen models from seven families. Dimension uses 192 contexts per model; shape uses a 48-context exact subset. Dimension and shape errors are reported separately.
Procedure in the paper: Evaluate the fixed probability-only and read-out-weighted predictors on the same declared model/context cells, retaining separate error definitions and exact-spectrum subsets.
Effective dimension
2,688 model–context observations: 14 models × 192 contexts. Below the diagonal favours the weighted profile; above favours probability-only. This endpoint asks how many directions are resolved.
Effective dimension counts distinguishable directions at a chosen resolution.
Spectrum shape
672 observations on the exact 48-context subset. This endpoint asks about the shape across spectral ranks, a different target from effective dimension.
The exponent describes how quickly eigenvalues decrease with rank. A smaller exponent error means the predicted and measured rates of decline are closer.
Code and data
v0.1.0 · 1.1 MB · View source on GitHub ↗
Matched effective-dimension and spectral-shape measurements for 14 models on 192 fixed contexts, with 48 exact spectra per model, final SLQ instrument repairs and family-level sign-flip inference.
v0.1.0 · 57 KB · View source on GitHub ↗
The 24 reference spectra, three damping ratios, probability controls, five-model inheritance check and 45 generated read-out cases.
v0.1.0 · 431 KB · View source on GitHub ↗
Native and standardized frame certificates and the probability/readout/width tail factorial.
v0.1.0 · 88 KB · View source on GitHub ↗
Four-width matched Gaussian initialization null, trained readout captures and the actual step-zero checkpoint.
v0.1.0 · 62 KB · View source on GitHub ↗
Actual output-Fisher/profile discrepancies, frame premises and early/final decomposition on 11 checkpoints.
v0.1.0 · 92 KB · View source on GitHub ↗
Weighted language-mode partitions, specificity controls, readout bridge and singleton/head-cell anatomy.
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.