Symmetry Preserving Conformal Prediction for RCC-8 Relation Networks

Source abstract

Spatial relation predictors should respect geometric symmetry while representing un-certainty. We study relation networks in the Region Connection Calculus with eight base relations (RCC-8), combining averaging over square symmetries and pair reversal, scene-level split conformal calibration, and sound algebraic closure. We prove score equivariance and exact preservation of the complete-scene coverage event by closure for realizable ground truth. Exchangeable calibration and test scenes yield a finite-sample coverage guarantee without requiring a symmetry-invariant population. Experiments use 17,400 synthetic rectangle scenes, two classifier families, and three seeds. At nominal 90% scene coverage, the complete method obtains 89.00% empirical coverage with a multilayer perceptron and 89.13% with extremely randomized trees, with 1.554 and 1.689 labels per directed pair. Mean set sizes decrease by 6.71% and 3.81% relative to raw scene calibration; closure contributes modest additional reductions. After pair-marginal calibration, closure instead lowers pair coverage from 89.73% to 77.27% and from 90.38% to 81.50%. Increased noise or scene size compromises coverage when calibration thresholds remain unchanged. The findings identify when sound spatial propagation preserves a statistical guarantee and demonstrate why the calibration unit must match the structured prediction target.