Standard forward pass. The model's forward() method must be a standard tensor-in, logits-out computation. No problem-specific control flow (for-loops over digits, explicit carry variables, string manipulation) inside forward(). The autoregressive generation loop lives outside the model, exactly as it would for any language model.
Full Parameter Support: Because the final shortcut refinement (Step 3 above) uses A* on detailed maps within each cluster, all your specified parameters are naturally incorporated:
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Real game engines use this pattern (or its 3D cousin, the Octree) for broad-phase collision detection: the quadtree quickly identifies candidate pairs, and a more expensive narrow-phase check tests the actual geometry.