OUTPUT-AWARE CONFORMAL GEOMETRY FOR STRUCTURED NONLINEAR PARAMETRIC MODELS

Structured parametric models generate complete meshes from compact parameters, but conformal coverage alone does not control the spatial extent of a decoded prediction set. We introduce output-aware conformal geometry (OACG), which shapes parameter-space ellipsoids using the matrix geometric mean (GM) of residual precision and decoder sensitivity. Independent calibration and exact decoding give finite-sample marginal coverage of representable references under exchangeability, regardless of linearization accuracy. For full-rank outputs, the unregularized GM core minimizes a pooled-moment surrogate for linearized RMS extent up to a common scale. Rank-deficient joint outputs require a ridge; we compare one isotropic in parameter coordinates (GM-I) with one isotropic in residual-normalized coordinates (GM-R). At nominal $90\%$ coverage, both variants reduce decoded RMS extent against additive fusion in all five primary mesh settings. GM-R improves on additive fusion in all seven primary joint settings, whereas GM-I trails it on the three SMPL joint settings. From matched to participant-disjoint HOT3D evaluation, GM-I's extent increases by $1.6$–$9.9\%$, versus $22.8$–$58.2\%$ for residual-only, additive, and GM-R geometries; population composition and participant overlap change together. A learned metric is smaller on EMDB but requires an additional geometry head. OACG makes fusion and ridge placement explicit choices for the spatial efficiency of structured prediction.