F-INR: Functional Tensor Decomposition for Implicit Neural Representations

2025-03-27

AI Summary

High-dimensional implicit neural representations (INRs) suffer from prohibitive computational overhead due to monolithic network architectures, where cost scales exponentially with dimensionality. To address this, we propose F-INR—a functional tensor decomposition framework that decouples high-dimensional mappings into lightweight, axis-specific subnetworks and composes them via functional tensor decompositions (CP, TT, or Tucker). This constitutes the first reformulation of INR learning from a *function decomposition* perspective. F-INR is modular, architecture-agnostic, and decomposition-agnostic, enabling joint control over reconstruction fidelity and inference speed. Experiments demonstrate a 100× training acceleration for video modeling with a 3.4 dB PSNR gain; significant improvements in compression efficiency, physical simulation accuracy, and 3D geometry reconstruction fidelity are also achieved across diverse benchmarks.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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 $100 imes$ 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.

Problem

• Reduces computational cost in high-dimensional INR models
• Decomposes high-dimensional tasks into lightweight sub-networks
• Improves accuracy and speed in signal modeling

Innovation

• Functional tensor decomposition for high-dimensional tasks
• Lightweight axis-specific sub-networks for specialized learning
• Modular architecture-agnostic framework with tensor operations