Periodic activations such as sine preserve high-frequency information in implicit neural representations (INRs) through their oscillatory structure, but often suffer from gradient instability and limited control over multi-scale behavior. We introduce the Hyperbolic Oscillator with Saturation Control (HOSC) activation, $\text{HOSC}(x) = \tanh\bigl(β\sin(ω_0 x)\bigr)$, which exposes an explicit parameter $β$ that controls the Lipschitz bound of the activation by $βω_0$. This provides a direct mechanism to tune gradient magnitudes while retaining a periodic carrier. We provide a mathematical analysis and conduct a comprehensive empirical study across images, audio, video, NeRFs, and SDFs using standardized training protocols. Comparative analysis against SIREN, FINER, and related methods shows where HOSC provides substantial benefits and where it achieves competitive parity. Results establish HOSC as a practical periodic activation for INR applications, with domain-specific guidance on hyperparameter selection. For code visit the project page https://hosc-nn.github.io/ .

翻译：诸如正弦函数等周期性激活通过其振荡结构在隐式神经表示（INRs）中保留高频信息，但常面临梯度不稳定性和对多尺度行为控制有限的问题。我们引入具有饱和控制的双曲振荡器（HOSC）激活函数：$\text{HOSC}(x) = \tanh\bigl(β\sin(ω_0 x)\bigr)$，该函数显式地引入参数 $β$，通过 $βω_0$ 控制激活函数的Lipschitz界。这提供了一种在保留周期性载波的同时直接调节梯度幅值的机制。我们进行了数学分析，并使用标准化训练协议在图像、音频、视频、NeRFs和SDFs等任务上开展了全面的实证研究。与SIREN、FINER及相关方法的对比分析表明，HOSC在某些场景下能带来显著优势，而在其他场景下则达到竞争性相当的水平。研究结果确立了HOSC作为INR应用中一种实用的周期性激活函数，并提供了针对特定领域的超参数选择指导。代码请访问项目页面 https://hosc-nn.github.io/ 。