This supplementary package contains the Appendix and Video Demonstrations accompanying the paper.

Appendix

Provides detailed formulation justifications, and dataset details beyond the main paper.

- Video Demonstrations

Video demonstrations are organized into four folders corresponding to evaluation environments:

 - Seen

- Unseen Placement

- Unseen Shape

- Unseen Color

Each folder contains four videos comparing different methods on the same task:

- Baseline Pi0 (pi0.mp4)

- System 2 as Gemini (gemini.mp4)

- System 2 as Gemini with Failure Prompt (gemini_failure.mp4)

- Ours (VINE) (ours.mp4)

These demonstrations highlight qualitative differences in planning and execution across baselines and our method under varying generalization challenges.