Affine-Equivariant Kernel Space Encoding for NeRF Editing

Neural scene representations achieve high-fidelity rendering by encoding 3D scenes as continuous functions, but their latent spaces are typically implicit and globally entangled, making localized editing and physically grounded manipulation difficult. While several works introduce explicit control structures or point-based latent representations to improve editability, these approaches often suffer from limited locality, sensitivity to deformations, or visual artifacts. In this paper, we introduce Affine-Equivariant Kernel Space Encoding (EKS), a spatial encoding for neural radiance fields that provides localized, deformation-aware feature representations. Instead of querying latent features directly at discrete points or grid vertices, our encoding aggregates features through a field of anisotropic Gaussian kernels, each defining a localized region of influence. This kernel-based formulation enables stable feature interpolation under spatial transformations while preserving continuity and high reconstruction quality. To preserve detail without sacrificing editability, we further propose a training-time feature distillation mechanism that transfers information from multi-resolution hash grid encodings into the kernel field, yielding a compact and fully grid-free representation at inference. This enables intuitive, localized scene editing directly via Gaussian kernels without retraining, while maintaining high-quality rendering.