mlsanityData to 14 Oct 2026

F-INR: Functional Tensor Decomposition for Implicit Neural Representations

arXiv 2503.21507 ↗First posted 27 Mar 2025cs.LGcited by 7

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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

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

57 of 101 references.

References · 57

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38 more
  1. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 700
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
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  16. 2016Tensor Ring Decompositioncited by 127
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  18. 2021A Structured Dictionary Perspective on Implicit Neural Representationscited by 100
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  38. 2024Functional Tensor Decompositions for Physics-Informed Neural Networkscited by 13

50 most cited of 57 All 57 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 5.

7 papers.

  1. 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectivescited by 4
  2. 2025RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physicscited by 1
  3. 2026FUTON: Fourier Tensor Network for Implicit Neural Representationscited by 1
  4. 2026Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recoverycited by 1
  5. 2026SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operatorscited by 1
  6. 2026Learning Spatial-Spectral Refinement and Calibrating Complementary Observations for Hyperspectral Image Super-Resolutioncited by 0
  7. 2026FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernelcited by 0