# Strivec: Sparse Tri-Vector Radiance Fields

arXiv: https://arxiv.org/abs/2307.13226 · HTML: https://mlsanity.com/paper/2307.13226/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 48 references that are in the map.
- First posted on arXiv 25 Jul 2023.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)

## Built on by (most cited first, 28 of 28)

- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [GS-LRM: Large Reconstruction Model for 3D Gaussian Splatting](https://mlsanity.com/paper/2404.19702/) (2024)
- [ContextGS: Compact 3D Gaussian Splatting with Anchor Level Context Model](https://mlsanity.com/paper/2405.20721/) (2024)
- [GaussianFlow: Splatting Gaussian Dynamics for 4D Content Creation](https://mlsanity.com/paper/2403.12365/) (2024)
- [Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration](https://mlsanity.com/paper/2403.11056/) (2024)
- [Spectrally Pruned Gaussian Fields with Neural Compensation](https://mlsanity.com/paper/2405.00676/) (2024)
- [Compact 3D Gaussian Splatting for Static and Dynamic Radiance Fields](https://mlsanity.com/paper/2408.03822/) (2024)
- [ZeroRF: Fast Sparse View 360deg Reconstruction with Zero Pretraining](https://mlsanity.com/paper/2312.09249/) (2023)
- [F-3DGS: Factorized Coordinates and Representations for 3D Gaussian Splatting](https://mlsanity.com/paper/2405.17083/) (2024)
- [Optimized Minimal 3D Gaussian Splatting](https://mlsanity.com/paper/2503.16924/) (2025)
- [Learning-based Multi-View Stereo: A Survey](https://mlsanity.com/paper/2408.15235/) (2024)
- [RoomDesigner: Encoding Anchor-latents for Style-consistent and Shape-compatible Indoor Scene Generation](https://mlsanity.com/paper/2310.10027/) (2023)
- [tttLRM: Test-Time Training for Long Context and Autoregressive 3D Reconstruction](https://mlsanity.com/paper/2602.20160/) (2026)
- [GS-Octree: Octree-based 3D Gaussian Splatting for Robust Object-level 3D Reconstruction Under Strong Lighting](https://mlsanity.com/paper/2406.18199/) (2024)
- [Expansive Supervision for Neural Radiance Field](https://mlsanity.com/paper/2409.08056/) (2024)
- [SpeeDe3DGS: Speedy Deformable 3D Gaussian Splatting with Temporal Pruning and Motion Grouping](https://mlsanity.com/paper/2506.07917/) (2025)
- [NeLF-Pro: Neural Light Field Probes for Multi-Scale Novel View Synthesis](https://mlsanity.com/paper/2312.13328/) (2023)
- [TK-Planes: Tiered K-Planes with High Dimensional Feature Vectors for Dynamic UAV-based Scenes](https://mlsanity.com/paper/2405.02762/) (2024)
- [NGP-RT: Fusing Multi-Level Hash Features with Lightweight Attention for Real-Time Novel View Synthesis](https://mlsanity.com/paper/2407.10482/) (2024)
- [Text-Image Conditioned 3D Generation](https://mlsanity.com/paper/2603.21295/) (2026)
- [G-NeLF: Memory- and Data-Efficient Hybrid Neural Light Field for Novel View Synthesis](https://mlsanity.com/paper/2409.05617/) (2024)
- [FIPER: Factorized Features for Robust Image Super-Resolution and Compression](https://mlsanity.com/paper/2410.18083/) (2024)
- [Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization](https://mlsanity.com/paper/2506.22134/) (2025)
- [Map2World: Segment Map Conditioned Text to 3D World Generation](https://mlsanity.com/paper/2605.00781/) (2026)
- [Neural Field Classifiers via Target Encoding and Classification Loss](https://mlsanity.com/paper/2403.01058/) (2024)
- [S3-SLAM: Sparse Tri-plane Encoding for Neural Implicit SLAM](https://mlsanity.com/paper/2404.18284/) (2024)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)

## Abstract (arXiv)

We propose Strivec, a novel neural representation that models a 3D scene as a radiance field with sparsely distributed and compactly factorized local tensor feature grids. Our approach leverages tensor decomposition, following the recent work TensoRF, to model the tensor grids. In contrast to TensoRF which uses a global tensor and focuses on their vector-matrix decomposition, we propose to utilize a cloud of local tensors and apply the classic CANDECOMP/PARAFAC (CP) decomposition to factorize each tensor into triple vectors that express local feature distributions along spatial axes and compactly encode a local neural field. We also apply multi-scale tensor grids to discover the geometry and appearance commonalities and exploit spatial coherence with the tri-vector factorization at multiple local scales. The final radiance field properties are regressed by aggregating neural features from multiple local tensors across all scales. Our tri-vector tensors are sparsely distributed around the actual scene surface, discovered by a fast coarse reconstruction, leveraging the sparsity of a 3D scene. We demonstrate that our model can achieve better rendering quality while using significantly fewer parameters than previous methods, including TensoRF and Instant-NGP.