PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling

A new framework called PRISM aims to improve how researchers model anatomical shapes and their uncertainties, according to a paper posted on the arXiv preprint server. The method combines implicit neural representations with statistical shape analysis to capture spatially varying dynamics that global time-warping approaches often miss. The paper, authored by Yining Jiao and submitted in 2026, introduces PRISM as a 3D probabilistic neural representation for interpretable shape modeling [1][2]. The framework models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations [1][2]. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation [1][2]. Experiments on three synthetic datasets and one clinical dataset demonstrated the framework's performance across tasks including modeling shape evolution, personalized shape prediction, and anomaly detection, while providing interpretable and clinically meaningful uncertainty estimates [1][2]. The manuscript was first posted on February 12, 2026, as version one, with a file size of 3,639 KB, and a revised second version followed on June 16, 2026, at 3,760 KB [1]. The work appears on arXiv, an open-access repository of electronic preprints that, as of November 2024, receives about 24,000 submissions per month and has hosted more than two million articles since its launch in 1991 [7]. arXiv papers are moderated but not peer-reviewed, and the platform has become a primary distribution channel in fields such as mathematics, physics, and computer science [7]. The repository also supports community-developed tools through its arXivLabs framework, which provides tabs on article pages for features such as bibliographic exploration, code discovery, and recommendation engines [5][6].