On the Structural Failure of Chamfer Distance in 3D Shape Optimization

Chamfer distance is the standard training loss for point cloud reconstruction, completion, and generation, yet directly optimizing it can produce worse Chamfer values than not optimizing it at all. We show that this paradoxical failure is gradient-structural. The per-point Chamfer gradient creates a many-to-one collapse that is the unique attractor of the forward term and cannot be resolved by any local regularizer, including repulsion, smoothness, and density-aware re-weighting. We derive a necessary condition for collapse suppression: coupling must propagate beyond local neighborhoods. In a controlled 2D setting, shared-basis deformation suppresses collapse by providing global coupling; in 3D shape morphing, a differentiable MPM prior instantiates the same principle, consistently reducing the Chamfer gap across 20 directed pairs with a 2.5$\times$ improvement on the topologically complex dragon. The presence or absence of non-local coupling determines whether Chamfer optimization succeeds or collapses. This provides a practical design criterion for any pipeline that optimizes point-level distance metrics.

CulinaryCut-VLAP: A Vision-Language-Action-Physics Framework for Food Cutting via a Force-Aware Material Point Method

Food cutting is a highly practical yet underexplored application at the intersection of vision and robotic manipulation. The task remains challenging because interactions between the knife and deformable materials are highly nonlinear and often entail large deformations, frequent contact, and topological change, which in turn hinder stable and safe large-scale data collection. To address these challenges, we propose a unified framework that couples a vision-language-action (VLA) dataset with a physically realistic cutting simulator built on the material point method (MPM). Our simulator adopts MLS-MPM as its computational core, reducing numerical dissipation and energy drift while preserving rotational and shear responses even under topology-changing cuts. During cutting, forces and stress distributions are estimated from impulse exchanges between particles and the grid, enabling stable tracking of transient contact forces and energy transfer. We also provide a benchmark dataset that integrates diverse cutting trajectories, multi-view visual observations, and fine-grained language instructions, together with force--torque and tool--pose labels to provide physically consistent training signals. These components realize a learning--evaluation loop that respects the core physics of cutting and establishes a safe, reproducible, and scalable foundation for advancing VLA models in deformable object manipulation.