用数学方法实现神经网络初始化零波动，图像重建更稳定可靠。
Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation
- 基于傅里叶分析设计确定性权重初始化，无需随机种子
- 在Kodak数据集上平均PSNR达67.18 dB，较最优基线提升21.30 dB
- 适合对结果可复现性要求高的科学计算与仿真场景
现有隐式神经表示（INR）方法存在随机初始化问题，导致不同运行间性能差异超过2.5 dB（约78%），严重影响科学计算与仿真的可复现性。为此，本文提出雅可比-安格正弦表示网络（JA-SIREN），一种基于经典谱分析的确定性初始化方案。通过计算目标信号的离散正弦变换（DST）并利用雅可比-安格展开，推导出两层正弦MLP的闭式权重，使网络初始频谱响应与目标信号精确匹配，无需随机种子或额外超参数调优。在Kodak数据集上，JA-SIREN实现平均PSNR 67.18 dB，较最佳基线提升21.30 dB，且无任何运行间方差，验证了谱信息引导初始化在正弦INR中更有效、更可复现。
原文摘要 · Abstract (English)
Existing implicit neural representation (INR) approaches suffer from stochastic initialization that does not guarantee consistent or high-quality performance across runs, with variations reaching more than 2.5 dB (~78%) in image regression. This variation is problematic for scientific computing and simulation, where result reproducibility is crucial. To address this problem, we present Jacobi-Anger Sinusoidal Representation Network (JA-SIREN), a deterministic initialization scheme for sinusoidal networks grounded in classical spectral analysis. By computing the Discrete Sine Transform (DST) of the target signal and leveraging the Jacobi-Anger expansion, we derive closed-form weights for a two-layer sinusoidal MLP that analytically match the network's initial spectral response to the target signal, requiring no random seed or additional hyperparameter tuning. On the Kodak dataset, JA-SIREN achieves a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline. This is achieved with zero run-to-run variance, confirming that spectrally-informed initialization is a more effective and reproducible alternative to stochastic initialization for sinusoidal INRs.
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