| # Cardinality / Range Dynamic Analysis | |
| ## 1. Data sources | |
| - Primary evaluation run: `20260426_145322` from `Evaluation/validation/runs/`. | |
| - Main metric file: `Evaluation\validation\runs\20260426_145322\summaries\validation_details__all_datasets.jsonl`. | |
| - Supporting files: `README.md`, paper sections under `Paper/69b27219c555c38a69bb2156/sections/`, `doc/synthetic_data_scoring_protocol_v0_4.md`, and `src/evaluation/synthetic_validation_v4.py`. | |
| - Coverage after normalization and deduplication: `51` datasets, `14` normalized models, `496` dataset-model assets, and `33815` column-level result units. | |
| - Missing coverage remains non-trivial for several generators, especially `codi`, `forestdiffusion`, and `tabdiff`. | |
| ## 2. Metric interpretation | |
| - In this repository, `cardinality/range` is one of the four Validation-layer channels, separate from analytics families and classical distance-based fidelity. | |
| - The discrete profile probes whether synthetic data preserves real observed support in non-continuous columns. In implementation terms, the official dataset-level score averages a column-risk indicator and a value-level missing-support indicator. | |
| - The continuous profile probes whether synthetic data preserves the real range envelope for continuous columns using per-column min/max deviation penalties. | |
| - For this analysis, discrete dynamic difficulty is tied to real distinct-count scale, while continuous dynamic difficulty is tied to real range width. This makes the probe difficulty-sensitive rather than treating all columns as equally hard. | |
| - The cleaned unit table keeps official channel scores as references, but the discrete column-level `score` used in bucket analysis is a derived support-retention ratio from the official per-column counts because the official implementation only exposes the two discrete indicators at dataset level. | |
| ## 3. Dynamic bucket construction | |
| - Discrete channel: absolute log-style buckets over `real_distinct_count` = `1-10`, `11-30`, `31-100`, `101-300`, `301-1000`, `>1000`. | |
| - Continuous channel: quantile buckets over `log10(real_range_width)` because raw widths are not directly comparable across datasets with different units and scales. | |
| - Low/high dynamic groups: discrete uses the first two versus last two buckets; continuous uses the bottom two versus top two quantile buckets. | |
| - Analysis unit: column-level whenever per-column details exist. This holds for both discrete and continuous branches in the selected validation run. | |
| ## 4. Main findings | |
| 1. The validation probe is difficulty-sensitive. Model separation widens in hard regimes: `8` models lose more than `0.05` absolute score when moving from their own overall average to the high-dynamic subset. | |
| 2. The numerically highest high-dynamic score belongs to `forestdiffusion` (`0.920`), but that result comes from only `17` datasets. Among broadly covered models (`n_datasets >= 30`), `tabpfgen` is the strongest high-dynamic performer at `0.890`. | |
| 3. Overall averages do hide failure modes. The clearest broad-coverage examples are `bayesnet` (0.932 -> 0.643); `realtabformer` (0.873 -> 0.641). Both models look strong in aggregate, but their high-dynamic means are much lower once the analysis equal-weights the discrete and continuous hard regimes. | |
| 4. Discrete versus continuous difficulty is not symmetric. The discrete branch is much sharper: mean score falls from `0.671` in the `1-10` bucket to `0.345` in the `>1000` bucket. By contrast, continuous bucket means stay within `0.617` to `0.770`, so range-width difficulty is more model-specific than uniformly monotone. | |
| 5. Dataset-level difficulty matters, but not through one scalar alone. The hardest dataset by mean score is `c13` (`mean_score=0.171`), and the largest across-model spread appears on `c10` (`score range=1.000`), which shows that some datasets amplify ranking differences much more than others even when their average dynamic intensity is not maximal. | |
| 6. The most fragile discrete and continuous models are not necessarily the same: discrete drop is largest for `bayesnet`, while continuous drop is largest for `arf`. | |
| ## 5. Suggested paper text | |
| Cardinality/range validation reveals a difficulty-sensitive structural failure mode that is largely hidden by aggregate fidelity summaries. When columns are easy, many generators appear similar. Once the benchmark moves into high-cardinality support or wide-range envelope regimes, however, model behavior diverges sharply. This is exactly the kind of integrity stress that matters for downstream analytics built on grouping, slicing, ranking, and thresholding over real schema columns. | |
| The discrete and continuous branches surface different weaknesses. In the current panel, high-cardinality support is the clearer global stressor: discrete support-retention falls sharply once real distinct counts leave the low-cardinality regime, and several generators that rank near the top overall collapse on the hardest discrete buckets. Continuous range-width behavior is still informative, but it is less uniformly monotone and instead separates models in a more generator-specific way. | |
| Most importantly, overall validation averages can mask high-dynamic failures. Several generators that look competitive in aggregate lose substantial score once evaluation is restricted to the structurally hardest columns. This supports the broader benchmark claim that synthetic-data evaluation cannot stop at generic similarity or pooled averages; it must test whether generators preserve the structures that downstream analytics depend on most. | |
| ## 6. Suggested figure captions | |
| - Figure 1: Dynamic response curves for validation-layer cardinality/range. Scores are plotted against real-data difficulty buckets, showing that model gaps widen as support cardinality or range width increases. | |
| - Figure 2: Low-versus-high dynamic slope plot for the discrete and continuous branches. Steeper downward slopes indicate generators whose apparent average fidelity hides hard-regime brittleness. | |
| - Figure 3: Compact dataset-by-model heatmaps for a filtered representative subset. The figure keeps the hardest and easiest datasets from the panel, but displays them in canonical dataset order so the dataset lookup is stable across revisions. | |
| - Figure 4: Overall average versus high-dynamic performance. Points far below the equality line are models whose aggregate validation scores overstate robustness in the hardest structural regimes. | |
| ## 7. Limitations | |
| - The selected run is the highest-coverage unified validation run in the repository, but it is still not a complete `51 × 14` panel; missing generator coverage affects confidence for sparse models. | |
| - The discrete unit score used for dynamic buckets is a derived support-retention ratio based on the official per-column support-loss counts, not a separately emitted protocol primitive. | |
| - Continuous dynamic buckets rely on quantiles of log-width because raw numerical ranges are not directly comparable across datasets with different measurement units. | |
| - Column-level analysis is the right unit for difficulty sensitivity, but it does not exactly match the official dataset-level discrete aggregation rule, which mixes equal-weighted column risk and globally weighted missing-support ratios. | |
| ## 8. Connection to the project claim | |
| - The README argues that synthetic-data evaluation must move beyond asking whether synthetic rows merely resemble real rows under classical distances. | |
| - This analysis supports that claim in a concrete way: even inside the Validation layer, a seemingly simple structural probe already exposes failures that pooled averages can hide. | |
| - High-cardinality support and wide range envelopes are exactly the kinds of structural preconditions that downstream SQL analytics rely on. If those fail, the synthetic table can still look statistically plausible while being analytically unreliable. | |
| ## 9. Representative failure cases | |
| - `c12` / `cdtd` / `continuous` / `height` / `Q5`: score `0.000`; invalid synthetic range envelope. | |
| - `c12` / `cdtd` / `continuous` / `width` / `Q5`: score `0.000`; invalid synthetic range envelope. | |
| - `c13` / `arf` / `continuous` / `caseid` / `Q5`: score `0.000`; range over-expansion on both sides. | |
| - `c13` / `cdtd` / `continuous` / `caseid` / `Q5`: score `0.000`; invalid synthetic range envelope. | |
| - `c14` / `cdtd` / `continuous` / `id` / `Q5`: score `0.000`; invalid synthetic range envelope. | |
| - `c14` / `cdtd` / `discrete` / `nom_7` / `>1000`: score `0.000`; full real-support collapse. | |
| - `c14` / `cdtd` / `discrete` / `nom_8` / `>1000`: score `0.000`; full real-support collapse. | |
| - `c14` / `cdtd` / `discrete` / `nom_9` / `>1000`: score `0.000`; full real-support collapse. | |
| - `c14` / `tabsyn` / `discrete` / `nom_7` / `>1000`: score `0.000`; full real-support collapse. | |
| - `c14` / `tabsyn` / `discrete` / `nom_8` / `>1000`: score `0.000`; full real-support collapse. | |