# F-INR: Functional Tensor Decomposition for Implicit Neural Representations

arXiv: https://arxiv.org/abs/2503.21507 · HTML: https://mlsanity.com/paper/2503.21507/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 101 references that are in the map.
- First posted on arXiv 27 Mar 2025.

## Builds on (most cited first, 30 of 57)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [I M Avatar: Implicit Morphable Head Avatars from Videos](https://mlsanity.com/paper/2112.07471/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [3D Neural Scene Representations for Visuomotor Control](https://mlsanity.com/paper/2107.04004/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)

## Built on by (most cited first, 7 of 7)

- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physics](https://mlsanity.com/paper/2510.06020/) (2025)
- [FUTON: Fourier Tensor Network for Implicit Neural Representations](https://mlsanity.com/paper/2602.13414/) (2026)
- [Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2603.01034/) (2026)
- [SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators](https://mlsanity.com/paper/2606.11518/) (2026)
- [Learning Spatial-Spectral Refinement and Calibrating Complementary Observations for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2609.05303/) (2026)
- [FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel](https://mlsanity.com/paper/2610.04212/) (2026)

## Abstract (arXiv)

Implicit Neural Representations (INRs) model signals as continuous, differentiable functions. However, monolithic INRs scale poorly with data dimensionality, leading to excessive training costs. We propose F-INR, a framework that addresses this limitation by factorizing a high-dimensional INR into a set of compact, axis-specific sub-networks based on functional tensor decomposition. These sub-networks learn low-dimensional functional components that are then combined via tensor operations. This factorization reduces computational complexity while additionally improving representational capacity. F-INR is both architecture- and decomposition-agnostic. It integrates with various existing INR backbones (e.g., SIREN, WIRE, FINER, Factor Fields) and tensor formats (e.g., CP, TT, Tucker), offering fine-grained control over the speed-accuracy trade-off via the tensor rank and mode. Our experiments show F-INR accelerates training by up to 20× and improves fidelity by over num6.0 dB PSNR compared to state-of-the-art INRs. We validate these gains on diverse tasks, including image representation, 3D geometry reconstruction, and neural radiance fields. We further show F-INR's applicability to scientific computing by modeling complex physics simulations. Thus, F-INR provides a scalable, flexible, and efficient framework for high-dimensional signal modeling. Project page: https://f-inr.github.io