Common-Center Geometry and Certified Radial Reconstruction for Energy-Form Full Conformal Regions

arXiv:2608.24964 · stat.ML, cs.LG, stat.ME · Submitted 2026-08-25 · Read on arXiv

stat.ML, cs.LG, stat.ME

Submitted: 2026-08-25

Updated: 2026-09-01

Comments: 29 pages, 3 figures. v2: tightened the radial certificate and added a staged numerical study of certificate tightness and robust nonconvexity diagnostics; conclusions and scope updated. Companion Lean 4 formalization and audited release: https://github.com/riasleyfung/fullcp-geometry-formal/tree/arxiv-v2-release

Code: https://github.com/riasleyfung/fullcp-geometry-formal

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Conformal Prediction — 7× in this paper · explained in 5 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Exchangeability — 3× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• Approximate full conformal prediction in an RKHS
• Approximate full-conformal multi-task regression with reproducing kernels
• CRPS-Optimal Binning for Univariate Conformal Regression

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• One Permutation Is All You Need: Fast, Deterministic Feature Importance and Model Stress-Testing
• Online Conformal Prediction for Non-Exchangeable Panel Data
• Deep Time-Series Forecasting in 10 Years: A Survey