F-INR: Functional Tensor Decomposition for Implicit Neural Representations
This provides a scalable solution for high-dimensional signal modeling in fields like video processing and 3D reconstruction, though it is incremental as it builds on existing INR methods.
The paper tackles the computational inefficiency of Implicit Neural Representations (INR) for high-dimensional data by proposing F-INR, a framework that uses functional tensor decomposition to break tasks into lightweight sub-networks, resulting in 100× faster training on video tasks and a 3.4 dB PSNR improvement.
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.