# 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`.