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.

翻译：隐式神经表示（INR）已成为利用神经网络将离散信号编码为连续可微函数的强大工具。然而，这些模型通常依赖单一架构来表示高维数据，导致计算成本随维度增长而急剧增加。我们提出F-INR框架，该框架通过函数张量分解重构INR学习过程，将高维任务分解为轻量化的轴向特定子网络。每个子网络学习一个低维数据分量（如空间或时间分量），随后通过张量运算组合这些分量，从而降低前向传播复杂度，并通过专业化学习提升精度。F-INR采用模块化设计，因此具备架构无关性，可与MLP、SIREN、WIRE或其他先进INR架构兼容。同时支持分解方式无关性，兼容CP、TT及Tucker分解模式，用户可通过自定义秩实现速度-精度调控。实验表明，F-INR在视频任务中的训练速度比现有方法快$100\times$，同时获得更高的保真度（PSNR提升+3.4 dB）。在图像压缩、物理仿真和三维几何重建任务中亦取得类似优势。F-INR由此为高维信号建模提供了一种可扩展、灵活的新解决方案。