用於高效高保真表示之遞迴正弦波隱式神經表示

摘要

我們研究正弦遞迴作為隱式神經表示中諧波頻譜增強的迭代機制。我們的分析揭示，正弦激活函數會產生諧波線譜，從而從頻譜角度解釋了遞迴展開如何有效增強有效頻譜支持。我們通過一個共享的正弦區塊實現此原理，該區塊通過迭代優化潛在表示。我們針對前饋式隱式神經表示、非正弦遞迴變體以及平衡態正弦模型，通過實驗驗證了所導致的頻譜行為。作為補充，我們在圖像和三維表示任務上評估了所提出的架構。在RGB圖像基準測試中，我們的方法以更少的參數和更少的優化步驟實現了比前饋基線更高的保真度，並進一步在超解析度、神經輻射場和符號距離函數任務中展現出良好的遷移表現。

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.