Recurrent Sinusoidal INRs for Efficient High-Fidelity Representation

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implicit-neural-representations sinusoidal-activation recurrent-networks spectral-analysis image-representation 3d-representation nerf

Summary

This paper introduces a recurrent sinusoidal architecture for implicit neural representations that achieves higher fidelity with fewer parameters and optimization steps by exploiting harmonic line spectrum enrichment through sinusoidal recurrence.

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.
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Source: https://huggingface.co/papers/2607.21485

Abstract

Westudysinusoidalrecurrenceasaniterativemechanismforharmonicspectralenrichmentinimplicitneuralrepresentations(INRs).Ouranalysisrevealsthatsinusoidalactivationsinduceaharmoniclinespectrum,providingaspectralaccountofhowrecurrentunrollingenrichestheeffectivespectralsupport.Werealizethisprinciplewithasharedsinusoidalblockthatiterativelyrefinesthelatentrepresentation.Weempiricallyvalidatetheresultingspectralbehavioragainstfeed-forwardINRs,non-sinusoidalrecurrentvariants,andequilibrium-stylesinusoidalmodels.Complementingthisanalysis,weevaluatetheproposedarchitectureacrossimageand3Drepresentationtasks.OnRGBimagebenchmarks,ourmethodachieveshigherfidelitythanfeed-forwardbaselineswithfewerparametersandfeweroptimizationsteps,anditfurthertransfersfavorablytosuper-resolution,NeRF,andSDFtasks.

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