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arXiv:2610.35904v1 Announce Type: new Abstract: Object-wise reconstruction increasingly inserts generated meshes into captured scenes as editable proxies for observed objects. This use creates a requirement absent from isolated-asset scores and pose estimates: at the captured metric state, the proxy should reproduce calibrated observations of the same instance. We present ObjectTwin, a scan-grounded measurement protocol that freezes the instance, cameras, scan-projected support and recorded depth, metric anchor, and evaluation denominator, then replaces only the object representation. The resulting asset correspondence gap measures lost observation agreement relative to scan-derived visible geometry without treating the scan as complete physical ground truth. Across two indoor RGB-D capture domains and two generation backends, visible, anchored generated assets lose 0.302-0.497 MaskIoU under this replacement. Every tested scene-level estimate is positive, while same-input generator preference reverses across capture domains. Coverage and overlap-depth analyses locate disagreement in both visible support and surface placement; the evaluated conservative pose refinement does not systematically recover it. These results establish capture correspondence as a separately measurable interface between generated-asset quality and stronger physical or task-level evaluation.
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arXiv:2610.36022v1 Announce Type: new Abstract: Image and video generators can produce spatially consistent visual content, but how to use this capability to improve spatial understanding remains underexplored. We study this problem from two perspectives: geometric supervision during training and explicit geometric evidence during inference.
arXiv:2610.36138v1 Announce Type: new Abstract: If rotating a problem never changes its answer, one might expect its best model to be rotation-invariant; we show that this fails, predictably and by an exact amount, when capacity is limited. A symmetry groups a model's directions into blocks of equally strong directions, a symmetric model must use each block whole, and when the budget cuts a block every optimal model breaks the symmetry.
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