# Equivariant Light Field Convolution and Transformer

arXiv: https://arxiv.org/abs/2212.14871 · HTML: https://mlsanity.com/paper/2212.14871/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 75 references that are in the map.
- First posted on arXiv 30 Dec 2022.

## Builds on (most cited first, 30 of 62)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Scene Representation Transformer: Geometry-Free Novel View Synthesis Through Set-Latent Scene Representations](https://mlsanity.com/paper/2111.13152/) (2021)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [SymRegFlow: Symmetry-Regularized Flow Matching for Video World Models](https://mlsanity.com/paper/2610.02726/) (2026)

## Abstract (arXiv)

3D reconstruction and novel view rendering can greatly benefit from geometric priors when the input views are not sufficient in terms of coverage and inter-view baselines. Deep learning of geometric priors from 2D images often requires each image to be represented in a 2D canonical frame and the prior to be learned in a given or learned 3D canonical frame. In this paper, given only the relative poses of the cameras, we show how to learn priors from multiple views equivariant to coordinate frame transformations by proposing an SE(3)-equivariant convolution and transformer in the space of rays in 3D. This enables the creation of a light field that remains equivariant to the choice of coordinate frame. The light field as defined in our work, refers both to the radiance field and the feature field defined on the ray space. We model the ray space, the domain of the light field, as a homogeneous space of SE(3) and introduce the SE(3)-equivariant convolution in ray space. Depending on the output domain of the convolution, we present convolution-based SE(3)-equivariant maps from ray space to ray space and to ℝ3. Our mathematical framework allows us to go beyond convolution to SE(3)-equivariant attention in the ray space. We demonstrate how to tailor and adapt the equivariant convolution and transformer in the tasks of equivariant neural rendering and 3D reconstruction from multiple views. We demonstrate SE(3)-equivariance by obtaining robust results in roto-translated datasets without performing transformation augmentation.