F-INR: Functional Tensor Decomposition for Implicit Neural Representations

• URL: http://arxiv.org/abs/2503.21507v1
• Date: Thu, 27 Mar 2025 13:51:31 GMT
• Title: F-INR: Functional Tensor Decomposition for Implicit Neural Representations
• Authors: Sai Karthikeya Vemuri, Tim Büchner, Joachim Denzler,
• Abstract summary: Implicit Representation (INR) has emerged as a powerful tool for encoding discrete signals into continuous, differentiable functions using neural networks.<n>We propose F-INR, a framework that reformulates INR learning through functional decomposition, breaking down high-dimensional tasks into lightweight, axis-specific sub-networks.
• Score: 7.183424522250937
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Implicit Neural Representation (INR) has emerged as a powerful tool for encoding discrete signals into continuous, differentiable functions using neural networks. However, these models often have an unfortunate reliance on monolithic architectures to represent high-dimensional data, leading to prohibitive computational costs as dimensionality grows. We propose F-INR, a framework that reformulates INR learning through functional tensor decomposition, breaking down high-dimensional tasks into lightweight, axis-specific sub-networks. Each sub-network learns a low-dimensional data component (e.g., spatial or temporal). Then, we combine these components via tensor operations, reducing forward pass complexity while improving accuracy through specialized learning. F-INR is modular and, therefore, architecture-agnostic, compatible with MLPs, SIREN, WIRE, or other state-of-the-art INR architecture. It is also decomposition-agnostic, supporting CP, TT, and Tucker modes with user-defined rank for speed-accuracy control. In our experiments, F-INR trains $100\times$ faster than existing approaches on video tasks while achieving higher fidelity (+3.4 dB PSNR). Similar gains hold for image compression, physics simulations, and 3D geometry reconstruction. Through this, F-INR offers a new scalable, flexible solution for high-dimensional signal modeling.

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