Robotic grinding is hard because it combines two problems that have different structures. You need to know what shape to remove, which is a geometric question. And you need to control the contact force during removal, which is a control question. Training a single model to handle both makes the learning problem enormous: every workpiece shape, every material hardness, every local geometry.
DecompGrind separates the two. The global cutting-surface plan is computed geometrically — compare the current shape to the target shape and calculate what material needs to go. No learning required. The local contact-force adaptation is learned from a small number of demonstrations, where a human shows the robot how to maintain safe force levels during the actual grinding pass.
The decomposition works because it restricts machine learning to the narrow scope where learning is actually needed. The geometry of material removal doesn't require experience — it requires subtraction. Whether a workpiece is round, flat, or complex doesn't change the geometry problem, only the solution. Force control during contact is where the physics gets uncertain: material hardness varies locally, tool wear changes the contact, vibrations couple unpredictably. That's where learning earns its keep.
The broader pattern: solving a hard problem often means first identifying which parts of it are actually hard. Geometry is deterministic. Contact is stochastic. The single model that handles both doesn't distinguish between them and wastes its capacity on the part that didn't need learning in the first place.