[NeurIPS Rebuttal] Statistical Support (Welch's Test & Multi-Seed) & Skip Connection Sweep

[Jiaqing-ASU]

Context:
Addressing concerns from Reviewer z8Q2 (W4) and Reviewer bRPK (3) regarding statistical significance (error bounds), and Reviewer Haek (Q3) regarding a continuous skip connection sweep.

Action Items:

• Table 2 Statistical Test: Calculate the p-value using Welch's t-test on the existing 5-seed data for Table 2 (Skip vs. No Skip) to prove significance.
• Table 3 Multi-Seed Error Bounds: Run 5 random seeds for the CNN regimes (Overfit/Underfit/Well-fit) and calculate the mean $\pm$ variance. (Note: Since NERSC is down, do this as a scaled-down local test on a small CNN).
• Skip Connection Sweep: On the same small local CNN, sweep the skip connection weight ($\alpha$) continuously (e.g., 0.0, 0.33, 0.66, 1.0) rather than a binary on/off.
• Generate updated tables/figures for the rebuttal response showing the monotonic decrease of SMAD as $\alpha$ increases.