给神经网络每个神经元动态分配频率，提升图像重建速度和精度。
FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representations
- 通过低秩门控路径为每个神经元分配随输入变化的频率。
- 在相同计算量下，2D图像重建PSNR提升最高达1dB，收敛更快。
- 适用于任意周期性激活函数，特别适合高频信号建模场景。
周期性隐式神经表示（INRs）如SIREN和FINER为每个神经元分配相同的全局频率，当局部信号内容变化时会浪费表示资源。本文提出FiRe（频率重参数化），通过不改变激活函数的前提下，重新参数化周期性INRs中每层神经元的频率。FiRe通过独立的低秩门控路径，使每个神经元具有受约束且依赖输入的频率，并适用于任何周期性激活函数。该门控机制作为隐式预条件器，在初始化阶段通过神经正切核（NTK）改善优化条件。更好的初始条件使优化更快收敛，且在固定计算预算下，重建的高频内容更贴近目标。在2D图像拟合任务中，FiRe相较于参数匹配基线，PSNR提升最高达+1dB（短训练预算时），性能随分辨率和训练预算变化，且可用NTK理论预测这些趋势。
原文摘要 · Abstract (English)
Periodic Implicit Neural Representations (INRs) such as SIREN and FINER assign every neuron, the same global frequency, spending the representational budget inefficiently when local signal content varies. We introduce FiRe (Frequency Reparameterization), that accelerates optimization by reparameterizing per-neuron frequency of periodic INRs without changing their underlying activation function. FiRe gives each neuron a bounded, input-dependent frequency via a separate low-rank gating path and is applicable to any periodic activation function. The gate acts as an implicit preconditioner that improves optimization conditioning at initialization via the Neural Tangent Kernel (NTK). This better-conditioned initialization makes optimization converge faster, and the high-frequency content of the reconstruction tracks the target more closely at a fixed computational budget. On 2D image fitting, FiRe increases PSNR over a parameter-matched baseline (up to +1 dB at short training budgets), with gains that vary with resolution and diminish at full convergence. We characterize how performance depends on resolution, rank, and training budget, and give an NTK account that predicts these trends.
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