# JacobiNeRF: NeRF Shaping with Mutual Information Gradients

arXiv: https://arxiv.org/abs/2304.00341 · HTML: https://mlsanity.com/paper/2304.00341/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 49 references that are in the map.
- First posted on arXiv 1 Apr 2023.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)

## Built on by (most cited first, 10 of 10)

- [Compliant Residual DAgger: Improving Real-World Contact-Rich Manipulation with Human Corrections](https://mlsanity.com/paper/2506.16685/) (2025)
- [Neural radiance fields in the industrial and robotics domain: applications, research opportunities and use cases](https://mlsanity.com/paper/2308.07118/) (2023)
- [PanopticNeRF-360: Panoramic 3D-to-2D Label Transfer in Urban Scenes](https://mlsanity.com/paper/2309.10815/) (2023)
- [Semantically-aware Neural Radiance Fields for Visual Scene Understanding: A Comprehensive Review](https://mlsanity.com/paper/2402.11141/) (2024)
- [LookOut: Real-World Humanoid Egocentric Navigation](https://mlsanity.com/paper/2508.14466/) (2025)
- [View-Consistent Hierarchical 3D Segmentation Using Ultrametric Feature Fields](https://mlsanity.com/paper/2405.19678/) (2024)
- [SG-NeRF: Neural Surface Reconstruction with Scene Graph Optimization](https://mlsanity.com/paper/2407.12667/) (2024)
- [A Unified Theory of Sinusoidal Activation Families for Implicit Neural Representations](https://mlsanity.com/paper/2502.00869/) (2025)
- [InfoNorm: Mutual Information Shaping of Normals for Sparse-View Reconstruction](https://mlsanity.com/paper/2407.12661/) (2024)
- [InfoGaussian: Structure-Aware Dynamic Gaussians through Lightweight Information Shaping](https://mlsanity.com/paper/2406.05897/) (2024)

## Abstract (arXiv)

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 highly-correlated 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 that emerges from our shaping to perform label propagation for semantic and instance segmentation. Our experiments show that a JacobiNeRF is more efficient in propagating annotations among 2D pixels and 3D points compared to NeRFs without mutual information shaping, especially in extremely sparse label regimes -- thus reducing annotation burden. The same machinery can further be used for entity selection or scene modifications.