Slot Count as an Ensemble Axis for Object-Centric Learning

Object-centric models decompose a scene into a fixed number of slots, yet the right number is rarely known. Too few slots merge objects, too many fragment them, and conventional inference commits to a single decomposition. We ask whether the decompositions that one model produces at different slot counts can instead be combined into a better one. We introduce PACE (Pairwise Agreement across Cardinality Ensembles), a two-part framework that answers this question positively. Prefix training samples a slot count at every step and activates the matching prefix of an ordered bank of slot initializers, so that a single checkpoint yields decompositions at many cardinalities from one encoder pass. Horizontal-Cut Consensus, a parameter-free readout, converts each soft partition into slot-invariant pairwise co-membership, averages this evidence, and cuts the resulting hierarchy into any requested number of regions, without slot matching, labels, or additional training. On COCO, PASCAL VOC2012, and MOVi-C, PACE improves FG-ARI by 4.67, 3.67, and 5.26 points over the standard seven-slot prediction, and mBO by 1.17 and 4.57 points on COCO and VOC2012. No single slot count recovers this grouping gain, even when the best one is chosen with evaluation labels. Controlled experiments trace the benefit to complementary errors. Coarse and fine requests fail in opposite ways, repeated sampling at one slot count saturates quickly, and a weak standalone partition can contribute more than a strong one. These results establish requested slot count as an ensemble axis and decouple the granularity of the grouping evidence from that of the final segmentation.