Recurrent Sinusoidal INRs for Efficient High-Fidelity Representation

2026-07-23

AI Summary

This work addresses the limited spectral expressivity and parameter inefficiency commonly observed in implicit neural representations (INRs). The authors propose a novel INR architecture based on a sinusoidal recurrent mechanism that, for the first time, integrates the harmonic line-spectrum properties of sine activations with unrolled recurrence. By employing shared recurrent sinusoidal blocks, the model iteratively refines latent representations to progressively enrich the harmonic spectrum. This approach substantially enhances spectral modeling capacity, achieving higher fidelity across multiple tasks—including RGB image reconstruction, super-resolution, NeRF, and signed distance field (SDF) representation—while consistently outperforming feedforward baselines with fewer parameters and reduced training iterations.

Abstract

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.

Problem

• Implicit Neural Representations
• Sinusoidal Recurrence
• Spectral Enrichment
• High-Fidelity Representation
• Efficiency

Innovation

• Recurrent INRs
• Sinusoidal Activation
• Spectral Enrichment
• Implicit Neural Representations
• Harmonic Spectrum