[2603.29860] GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates

Computer Science > Graphics arXiv:2603.29860 (cs) [Submitted on 12 Mar 2026] Title:GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates Authors:Samundra Karki, Adarsh Krishnamurthy, Baskar Ganapathysubramanian View a PDF of the paper titled GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates, by Samundra Karki and 2 other authors View PDF Abstract:Implicit Neural Representations (INRs) provide compact models of geometry, but it is unclear when their learned shapes can be edited without retraining. We show that the Gram operator induced by the INR's penultimate features admits deformation eigenmodes that parameterize a family of realizable edits of the SDF zero level set. A key finding is that these modes are not intrinsic to the geometry alone: they are reliably recoverable only when the Gram operator is estimated from sufficiently rich sampling distributions. We derive a single closed-form update that performs geometric edits to the INR without optimization by leveraging the deformation modes. We characterize theoretically the precise set of deformations that are feasible under this one-shot update, and show that editing is well-posed exactly within the span of these deformation modes. Comments: Subjects: Graphics (cs.GR); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) Cite as: arXiv:2603.29860 [cs.GR]   (or arXiv:2603.29860v1 [cs.GR] for this version)   https://doi.org/10.48550/arX...