arXiv:2611.05543v1 Announce Type: new Abstract: In multivariate conformal prediction, many nonconformity scores yield prediction sets with complex geometry (e.g., ellipsoids or density level sets) that are difficult to interpret and visualize. Hyperrectangles offer a practical alternative by providing one interval per output. We extend this notion to Cartesian products of arbitrary one-dimensional sets, which we call generalized hyperrectangles. We introduce a rectangularization framework that turns any continuous multivariate nonconformity score, or conditional density, into one yielding generalized hyperrectangular prediction sets with finite-sample coverage. We establish key geometric properties of our rectangularization framework and provide useful intuitions on generalized hyperrectangles. We further establish a representation theorem showing that a broad class of hyperrectangular conformal methods based on max-aggregated coordinate-wise scores can be interpreted as rectangularizations of implicit conditional densities. Through synthetic and real-world experiments, we quantify the efficiency cost of rectangularization, while highlighting its benefits, especially for practical applications of uncertainty quantification.