[NeurIPS Rebuttal] Ground-Truth Sanity Check: Rosenbrock Function Test

[Jiaqing-ASU]

Context:
Addressing concerns from Reviewer Haek (W2), Reviewer z8Q2 (W2), and Reviewer bRPK (4), as well as the AC's meta-review, regarding the need for a ground-truth sanity check for the SMAD metric.

Action Items:

• Evaluate Landscaper and SMAD on a parameterized high-dimensional Rosenbrock function.
• Generate a table or figure demonstrating how SMAD correlates with the mathematically known analytical properties (barrier heights, basin depths, global smoothness) of the function.
• Ensure the results clearly validate SMAD's behavior outside of the deep learning context.

[rostyhn]

Commit 6456184 adds the rosenbrock tests and visualizes them; a=1, b=100. The profiles for 2d and 5d behave as expected. 2D shows a single minima, while 5D shows the split minima that develop between dimensions 4 and 20D, well known behavior for this function.

2D profile of the Rosenbrock function 5D profile of the Rosenbrock function