Measure parameter shell geometry in paired Qwen3.5-2B checkpoints

model_shell/PROTOCOL.md

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+# Actual-model parameter clouds: frozen grouping and null protocol
+
+Assets: retained Qwen3.5-2B original15852e8c16360a2fea060d615a32b45270f8a8fc,
+and pure GSM8K GRPO LoRA seed0 at HF038d8be9bd0edd3883fa019651b02bdf65609468.
+Use the established read-only FP32 W+2BA wrapper. No training, GPU, new models,
+weight mutation, inference requirement or deletion. Every retained asset stays.
+
+## What constitutes a distribution
+
+A model has no unique canonical number of parameter distributions. Enumerate a
+fixed family, not "all possible distributions":
+1. Each ndim>=2 tensor flattened as [axis0, product(other axes)]: row vectors
+   and column vectors, when point count>=16 and feature dimension>=32.
+2. Decoder language/MTP full-attention Q and interleaved gate rows per query
+   head; K/V rows per KV head. GDN concatenated Q/K/V rows per corresponding head.
+   No claim that these groups are disjoint or iid; whole-matrix views overlap.
+3. Primary sample-size stratum has >=64 available points;16..63 is small-sample
+   descriptive only. One-dimensional norm/bias vectors have no cloud of vectors;
+   GDN kernel row dimension4 is low dimensional and excluded with explicit reason.
+   Vision parameters are covered by matrix/flattened views, not vision-head splits.
+
+Include all checkpoint components (language, vision and MTP). Per view choose
+up to512 point indices without replacement, split deterministically into calibration
+and held-out halves. Use full vector coordinates up to dimension8192; only larger
+vectors use a fixed random coordinate subset, labelled projected rather than full.
+Use identical indices, coordinates and null random draws for original/FT.
+No overlap-group parameter savings or total distribution counts are additive.
+
+## Centers and radius/scaling
+
+Analyze origin and calibration-mean centers separately. Fit R_max using calibration
+norms only; do not silently clip held-out points outside R_max. Also fit calibration
+RMS radius. Store held-out maximum, outside-radius mass and radial spread.
+
+Null A: uniform d-dimensional ball. Simulate the SAME center-fitting and calibration
+maximum/RMS fitting before held-out evaluation. For origin, also retain exact
+expected max-fitted null CDF a^d*n_cal/(n_cal+1), a<=1; log probabilities remain
+available and zero Monte Carlo hits are not exact zeros.
+Null B: independent coordinate-uniform box bounded by calibration min/max,
+including asymmetric coordinates. Fit its center/radii using its own calibration
+sample by exactly the same procedure. Record energy/range mismatch and held-out
+coordinate violations; this null is conditional on fitted bounds, not a statement
+that all real vectors lie inside that box.
+Null C: independent coordinate-uniform box with calibration mean mu and standard
+deviation sigma, bounds mu +/- sqrt(3)*sigma (sample variance ddof1). This matches
+first and diagonal second moments in its generating law. Use its own calibration
+and held-out center/max/RMS fits too; RMS-normalized comparisons target shape
+rather than a change of global scale. Matching diagonal moments is not covariance
+matching and does not preserve correlations.
+
+Use512 validation null draws (not iid model observations), same calibration count
+as each data cloud. Reuse isotropic-ball nulls only for identical dimension/count
+and center-fitting rules. Monte Carlo resolution/error must be stated. Fit both
+centers from the same raw draws where applicable; paired FT uses common randomness.
+
+## Metrics and interpretation
+
+Retain measured norm arrays, empirical CDF grids, max-normalized interior fractions
+at0.5/0.75/0.9/0.95/0.99 and outside1, RMS-normalized CDF from0.5 to1.5,
+median radial ratios and radial spread. Prefer probability-point differences over
+astronomical ratios against tiny a^d. Inspect positive AND negative CDF gaps:
+more inner tail plus more outer tail is not global inward stochastic dominance.
+
+Record exact zeros, coordinate energy participation (sum squares)^2/sum fourths,
+coordinate-variance participation, empirical covariance/second-moment participation
+via calibration Gram matrices. Label sample rank ceiling n_cal-1 (mean centered)
+or n_cal (origin); compare to equally sampled nulls, do not interpret the raw
+finite-sample participation as true intrinsic dimension.
+
+Report both full-radius and moment-controlled results for each center, whole-view
+and head subgroups, primary versus small sample/projection strata, original and
+changed72-LoRA-target groups. Unchanged parameter views can reuse identical results
+with explicit references rather than re-read/recompute. Results describe parameters,
+not activations, model quality, functional duplicates, or pruning gains.
+
+Execution budget: one CPU, 512 MiB RSS ceiling, 7200 seconds per invocation;
+checkpoint every group, resume without replacing completed groups. Any incomplete
+coverage is reported before interpretation. No numerical analysis runs locally.
+
+Illustrative radial CDFs use these fixed original/origin views, selected by module
+role before the census completes, not by the resulting similarity/interior score:
+language layer0 linear-attention Q head0, layer3 full-attention Q head0, and layer0
+MLP up-projection rows. Their plots are illustrations, not independent replications.