递归正弦INR用于高效高保真表示

摘要

我们研究正弦递归作为隐式神经表示中谐波频谱丰富的一种迭代机制。分析表明，正弦激活会诱发谐波线谱，从频谱角度解释了递归展开如何增强有效频谱支持。我们通过共享正弦块实现这一原理，该模块迭代优化潜在表示。我们针对前馈隐式神经网络、非正弦递归变体及平衡态正弦模型，实证验证了所得频谱行为。作为上述分析的补充，我们评估了所提出架构在图像和三维表示任务上的表现。在RGB图像基准测试中，我们的方法以更少的参数和更少的优化步骤实现了高于前馈基线的保真度，并进一步成功迁移至超分辨率、NeRF和SDF任务。

English

We study sinusoidal recurrence as an iterative mechanism for harmonic spectral enrichment in implicit neural representations (INRs). Our analysis reveals that sinusoidal activations induce a harmonic line spectrum, providing a spectral account of how recurrent unrolling enriches the effective spectral support. We realize this principle with a shared sinusoidal block that iteratively refines the latent representation. We empirically validate the resulting spectral behavior against feed-forward INRs, non-sinusoidal recurrent variants, and equilibrium-style sinusoidal models. Complementing this analysis, we evaluate the proposed architecture across image and 3D representation tasks. On RGB image benchmarks, our method achieves higher fidelity than feed-forward baselines with fewer parameters and fewer optimization steps, and it further transfers favorably to super-resolution, NeRF, and SDF tasks.