Shared-Basis Stability Insights

Main reading

On the shared support-oriented basis support3_score = mean(key_set_score, row_count_score, column_score), subgroup-size queries are more robust than internal-profile queries.

Query-level means: internal = 0.777, size = 0.818
Query-level medians: internal = 0.889, size = 1.000
Low-tail share <= 0.4: internal = 0.143, size = 0.129
High-score share >= 0.8: internal = 0.538, size = 0.632

Matched-panel interpretation

Comparing the two subgroup branches inside the same dataset-model panel avoids raw-score incomparability. Under this matched view, support3(size) - support3(internal) is positive on average.

Mean matched-panel delta: 0.011
Share of panels with size > internal: 0.437
Share of panels with size - internal >= 0.10: 0.126
This is therefore a distribution-level stability story, not a claim that size wins on every matched panel.

Model-facing interpretation

The models below look most like subgroup-scaffold preservers: they keep keys, row counts, and output structure more reliably on the size side than on the internal side.

TVAE: support advantage 0.035, key advantage 0.049. Reading: size-led scaffold preserver.
TabPFGen: support advantage 0.034, key advantage 0.030. Reading: size-led scaffold preserver.
TabDDPM: support advantage 0.027, key advantage 0.044. Reading: moderate size-led scaffold preserver.
CTGAN: support advantage 0.027, key advantage 0.031. Reading: moderate size-led scaffold preserver.

These models look less like clean size-led preservers:

ForestDiffusion: support advantage -0.011, key advantage -0.002. Reading: no clear scaffold edge.
ARF: support advantage -0.012, key advantage -0.001. Reading: no clear scaffold edge.
TabSyn: support advantage -0.020, key advantage 0.032. Reading: key retention without stable size scaffold.

A particularly informative mixed case:

TabSyn: support advantage -0.020 but key advantage 0.032. Reading: subgroup identities are often retained, but the row-count / table-scaffold side is not stable enough to turn that into a size-led advantage.

What ability is this really measuring?

subgroup_size_stability on the shared basis is mostly a subgroup scaffold preservation ability: whether the same groups appear, whether rough prevalence is retained, and whether result-table structure survives.
internal_profile_stability asks for a harder within-group analytical structure ability: preserving ranking, filtered subgroup summaries, local two-dimensional geometry, and group-specific contrast after the subgroup has already been identified.

Prefix pattern

The clearest size-led regime is m, where the shared-basis support advantage is largest.
c is the main caution regime: on the shared support basis it is roughly balanced or slightly internal-favored, so the size story should not be overstated as universal.
n still shows a positive support-side edge, but much smaller than m.
c: support delta -0.015, key delta -0.010, size > internal share 0.322.
m: support delta 0.032, key delta 0.056, size > internal share 0.626.
n: support delta 0.024, key delta 0.041, size > internal share 0.417.