JA-SIREN: Deterministic Initialization for Sinusoidal Networks via Spectral Matching

2026-06-08 · Source: cs.CV updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, long

Summary

Jacobi-Anger Sinusoidal Representation Network (JA-SIREN) is a novel, deterministic initialization scheme for sinusoidal implicit neural representations (INRs) that eliminates the performance variability inherent in stochastic initialization. Existing INR approaches suffer from run-to-run variations, reaching over 2.5 dB (~78%) in image regression, which is problematic for scientific reproducibility. JA-SIREN addresses this by leveraging the Discrete Sine Transform (DST) of the target signal and the Jacobi-Anger expansion to derive closed-form weights for a two-layer sinusoidal MLP. This process analytically matches the network's initial spectral response to the input, requiring no random seed or additional hyperparameter tuning. Experiments on the Kodak dataset show JA-SIREN achieving a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline (FM-FINER at 45.88 dB), with zero run-to-run variance. It also achieved a mean SSIM of 0.9999 and demonstrated superior performance in 1D audio regression.

Key takeaway

For Machine Learning Engineers developing implicit neural representations (INRs) for high-precision applications like medical imaging or scientific computing, you should prioritize deterministic initialization schemes such as JA-SIREN. This approach eliminates the significant run-to-run variability of stochastic methods, guaranteeing consistent, high-fidelity results. Adopting JA-SIREN ensures your models achieve superior reconstruction quality, with demonstrated PSNR gains exceeding 21 dB, and provides the crucial reproducibility required for rigorous scientific and professional deployments.

Key insights

Deterministic, spectrally-informed initialization for sinusoidal INRs dramatically enhances reconstruction quality and reproducibility over stochastic methods.

Principles

• Stochastic initialization limits INR reproducibility.
• Spectral matching improves INR reconstruction quality.
• Jacobi-Anger expansion enables deterministic weight derivation.

Method

JA-SIREN computes the Discrete Sine Transform (DST) of the target signal, retaining dominant frequency components. It then uses the Jacobi-Anger expansion to derive closed-form weights for a two-layer sinusoidal MLP, analytically matching the network's initial spectral response.

In practice

• Apply JA-SIREN for high-fidelity image compression.
• Use deterministic INRs in medical imaging.
• Employ JA-SIREN for reproducible scientific simulations.

Topics

• Implicit Neural Representations
• Deterministic Initialization
• Sinusoidal Networks
• Jacobi-Anger Expansion
• Discrete Sine Transform
• Image Regression

Best for: Research Scientist, Computer Vision Engineer, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CV updates on arXiv.org.