Recurrent Sinusoidal INRs for Efficient High-Fidelity Representation

We study sinusoidal recurrence as an iterative mechanism forharmonic spectral enrichment in implicit neural representations (INRs).Our analysis reveals that sinusoidal activations induce a harmonic linespectrum, providing a spectral account of how recurrent unrolling en-riches the effective spectral support. We realize this principle with ashared 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-stylesinusoidal models. Complementing this analysis, we evaluate the pro-posed architecture across image and 3D representation tasks. On RGBimage benchmarks, our method achieves higher fidelity than feed-forwardbaselines with fewer parameters and fewer optimization steps, and it fur-ther transfers favorably to super-resolution, NeRF, and SDF tasks.