Figure 5a,b; SI: anatomy
Spectral inheritance
A frozen profile predicts held-out spectra and effective-dimension curves in nine models across five external families, outperforming matched flat and shuffled controls.
A token profile predicts how many directions matter.
Each model predicts the next token from the text below. Compare the metric’s measured response with a prediction from weighted token probabilities.
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What is gained by retaining the profile?
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Frame certificates and the spectral tail
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Frequency structure at initialization and after training
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Certificates do not imply improving alignment during training
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Capture and structural quality of language partitions
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Testing fixed partitions on new contexts
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Methods and interpretation
576 model–context cells. Spectrum-shape comparisons use ranks 8–32 in a fixed standardised read-out representation; each interactive curve contains ten recorded resolution settings.
Procedure in the paper: Construct centred orthonormalised read-out rows, freeze the ordered weighted profile before exact spectrum access, evaluate the disjoint context battery, and calculate the declared rank-window and damping-grid errors.
Code and data
v0.1.0 · 75 KB · View source on GitHub ↗
Profile freezing, exact spectra, response curves and controls for 13 models on 128 contexts; the primary held-out comparison contains 576 model–context cells.
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.
v0.1.0 · 68 KB · View source on GitHub ↗
Eight-model local-core/crossover study and four-model nested-support/full-vocabulary audit.
v0.1.0 · 1.2 MB · View source on GitHub ↗
Fresh-context redistribution and cross-model partition agreement, with fixed calibration partitions and separate model downloads.
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.