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DOI 1.20 — A ground-truth-free binary classifier for Amplification Phase risk

View DOI 1.20 on Zenodo: https://doi.org/10.5281/zenodo.22968572

New DBBuilt on the current, join-free pipeline (build_notta_tta_comp_db.py), one independent database per model.

This series has established μ_stat as a model-specific, empirically-calibrated transition point marking SSIM's Amplification Phase — the region where the luminance term becomes hypersensitive to small absolute deviations between ground-truth mean brightness μ_gt and a reconstruction's own mean brightness μ_notta. Diagnosing whether a given block falls inside this region has so far required μ_gt itself, i.e. ground truth. This report tests whether a practitioner with only a model's reconstruction, no ground truth, can still obtain a useful risk signal using μ_notta alone.

Exact value estimation (μ_gt recovered from μ_notta) proves structurally unreliable: the best method tried across a wide range of regression, lookup-table, and hybrid variants improves at most ~65% of individual blocks, because μ_gt's underlying 8-bit pixel quantization makes its finest levels difficult to separate using μ_notta alone. Reframing the question as binary classification instead — is this block at risk, yes or no — sidesteps that identifiability problem entirely: since μ_stat falls partway through the quantization grid, every finer distinction below it is irrelevant to the binary question.

The classifier — verification_sql_final_4model_comp.sql

The identical query below repeats for all four models, only the μ_stat constant and database path change (shown once here for Upscayl Standard):

The merutan CTE — recovering μ_notta, within the Merutan Condition

The comp DB does not store μ_notta as a column; this CTE recovers it from ssim_l_notta via the smaller root of the quadratic form of SSIM's luminance term (the 2*mu_gt - SQRT(...) expression, solving L=(2μgtμnotta+C1)/(μgt2+μnotta2+C1) for μ_notta). The WHERE clause restricts to this report's "Merutan Condition" population: blocks where all eight GT-side comp_*_gt features equal exactly zero (a flat, texture-free GT region), and where TTA measurably changes the SSIM product (excluding blocks where TTA has no effect at all). Restricting to perfectly flat GT regions is what makes the coarser classification question tolerate μ_notta's imprecision, as explained above.

.open --readonly output_std/std_notta_tta_comp.duckdb

SELECT COUNT(*) AS n_total_blocks_in_db FROM blocks;

WITH merutan AS (
    SELECT
        mu_gt,
        (2*mu_gt - SQRT(POWER(2*mu_gt, 2)
            - 4*ssim_l_notta*(ssim_l_notta*(POWER(mu_gt,2)+0.0001) - 0.0001)))
            / NULLIF(2*ssim_l_notta, 0) AS mu_notta
    FROM blocks
    WHERE comp_sharpness_gt = 0 AND comp_edges_gt = 0
      AND comp_artifact_ringing_gt = 0 AND comp_artifact_block_gt = 0
      AND comp_contrast_gt = 0 AND comp_texture_gt = 0
      AND comp_entropy_gt = 0 AND comp_noise_gt = 0
      AND (ssim_l_tta*ssim_c_tta*ssim_s_tta) != (ssim_l_notta*ssim_c_notta*ssim_s_notta)
),

The labeled CTE and final SELECT — confusion matrix

labeled reduces both sides to a single boolean each: true_amp_phase asks whether the ground truth actually falls at or below μ_stat, and predicted_amp_phase asks the same question of the algebraically recovered μ_notta — filtering out the rare blocks where the expression under the square root is negative (no real solution, mu_notta IS NULL). Comparing the two, block by block, gives the confusion-matrix counts (true_positive, false_negative, false_positive, true_negative), from which accuracy_pct, recall_pct, and precision_pct are each computed as the usual percentage of the relevant denominator.

labeled AS (
    SELECT
        (mu_gt <= 0.0500) AS true_amp_phase,
        (mu_notta <= 0.0500) AS predicted_amp_phase
    FROM merutan
    WHERE mu_notta IS NOT NULL
)
SELECT
    COUNT(*) AS n_total,
    COUNT(*) FILTER (WHERE true_amp_phase) AS n_true_amp_phase,
    COUNT(*) FILTER (WHERE NOT true_amp_phase) AS n_true_stable,
    COUNT(*) FILTER (WHERE true_amp_phase AND predicted_amp_phase) AS true_positive,
    COUNT(*) FILTER (WHERE true_amp_phase AND NOT predicted_amp_phase) AS false_negative,
    COUNT(*) FILTER (WHERE NOT true_amp_phase AND predicted_amp_phase) AS false_positive,
    COUNT(*) FILTER (WHERE NOT true_amp_phase AND NOT predicted_amp_phase) AS true_negative,
    ROUND(COUNT(*) FILTER (WHERE true_amp_phase = predicted_amp_phase) * 100.0 / COUNT(*), 4) AS accuracy_pct,
    ROUND(COUNT(*) FILTER (WHERE true_amp_phase AND predicted_amp_phase) * 100.0
        / NULLIF(COUNT(*) FILTER (WHERE true_amp_phase), 0), 4) AS recall_pct,
    ROUND(COUNT(*) FILTER (WHERE true_amp_phase AND predicted_amp_phase) * 100.0
        / NULLIF(COUNT(*) FILTER (WHERE predicted_amp_phase), 0), 4) AS precision_pct
FROM labeled;

-- Repeats identically for SwinIR (mu_stat=0.0800), High-Fidelity
-- (mu_stat=0.0860), and Digital-Art (mu_stat=0.0750), each preceded
-- by its own .open line.

Results (Table 1)

All four models: n_total_blocks_in_db = 81,985,536 (unfiltered, identical across models). Evaluated as a confusion matrix against the true label (μ_gt ≤ μ_stat), over the full population (both classes present, not restricted to one side of the boundary):

Upscayl Standard (μ_stat=0.0500, n=1,053,322): 96.029% accuracy, 100.0% recall, 95.738% precision. SwinIR (μ_stat=0.0800, n=36,488): 100.0% accuracy, 100.0% recall, 100.0% precision. Upscayl High-Fidelity (μ_stat=0.0860, n=2,299,477): 99.7096% accuracy, 100.0% recall, 99.7074% precision. Digital-Art (μ_stat=0.0750, n=393,852): 99.9035% accuracy, 100.0% recall, 99.9013% precision.

All four models achieve 96%+ accuracy, with recall exactly 100.0% throughout — no true at-risk block is missed in any model — using a single untrained threshold, fully ground-truth-free at application time despite μ_notta itself being an algebraically recovered quantity rather than a directly stored column. μ_stat is calibrated from ground truth only once per model-and-dataset combination (this calibration was done against one specific dataset, NIH ChestX-ray8; whether the same values hold on a different dataset is untested); once that one-time calibration exists, the same threshold applies to any subsequent, ground-truth-free reconstruction on that same dataset. This is offered as a validated diagnostic method for a specific, narrow use case, not as a claim that ground-truth-free SSIM diagnosis is possible in general — see the full report for scope and caveats. A plain-language walkthrough of these results, with a photo-of-a-blank-wall analogy, is available on the GT-free diagnostic tools explainer page.