JacobiNeRF: NeRF Shaping with Mutual Information Gradients

We propose a method that trains a neural radiance field (NeRF) to encode not only the appearance of the scene but also semantic correlations between scene points, regions, or entities -aiming to capture their mutual co-variation patterns. In contrast to the traditional first-order photometric reconstruction objective, our method explicitly regularizes the learning dynamics to align the Jacobians of highlycorrelated entities, which proves to maximize the mutual information between them under random scene perturbations. By paying attention to this second-order information, we can shape a NeRF to express semantically meaningful synergies when the network weights are changed by a delta along the gradient of a single entity, region, or even a point. To demonstrate the merit of this mutual information modeling, we leverage the coordinated behavior of scene entities