Reconstruction Frontier Deep Dive

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This deep dive tracks the empirical frontier between baseline-normalized reconstruction loss and matched strategy router score.

The normalized reconstruction variants occupy the high-score, low-reconstruction-ratio region. The top mean matched strategy router score is dist_plus_tokcc_a0p5_b0p01_d50_lin50 at 0.8532 with baseline-normalized reconstruction 0.0379. Other top normalized settings have reconstruction ratios from 0.0331 to 0.0407 and matched scores from 0.8185 to 0.8465.

The raw ELBO baselines occupy the low-score, high-reconstruction-ratio region. Their mean matched strategy router scores are 0.4432 for raw_b1_lin100, 0.4419 for raw_b1_const, and 0.4396 for raw_b1_d50_lin50; their baseline-normalized reconstruction ratios are 1.0690, 1.0718, and 1.0712.

The highest individual runs by matched score include dist_norm_b0p01_d50_lin50, example_inv_surp_b0p01_const, three_way_equal_b0p01_d50_lin50, and dist_norm_b0p01_const. These runs combine near-ceiling final answer accuracy with router probe near 0.95 and posterior probe at or near 1.0.

Open empirical checks:

• Separate the reconstruction-ratio axis by task family to verify whether each synthetic family has the same frontier shape.
• Compare the frontier at matched wall-clock or training-step budgets, since schedules change the timing of beta pressure.
• Inspect whether the raw baseline's high reconstruction ratio is tied to logged raw-token scale, KL usage, or posterior probe collapse in specific families.