用函数张量分解让神经隐式表示更快更准
F-INR: Functional Tensor Decomposition for Implicit Neural Representations
- 将高维隐式网络拆成轴向子网络，通过张量运算组合
- 训练速度提升20倍，图像保真度提高6.0 dB以上PSNR
- 适配多种模型和张量格式，适合高维信号建模任务
隐式神经表示（INRs）将信号建模为连续可微函数，但传统单体INR随数据维度增长而计算开销剧增。本文提出F-INR，基于函数张量分解，将高维INR分解为一组紧凑的轴向子网络，学习低维函数分量并通过张量操作组合。该方法降低计算复杂度，同时提升表达能力。F-INR与架构和分解方式无关，可兼容SIREN、WIRE等主流INR骨干网络及CP、TT、Tucker等张量格式，通过调整张量秩与模式实现精度-速度的精细权衡。实验表明，F-INR训练加速达20倍，图像保真度提升超6.0 dB PSNR，且在图像表示、3D几何重建、神经辐射场等任务中表现优异。进一步验证其在复杂物理模拟建模中的适用性。F-INR为高维信号建模提供了高效、灵活、可扩展的框架。
原文摘要 · Abstract (English)
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 $20\times$ and improves fidelity by over \num{6.0} 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
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