提出HOSC激活函数，稳定梯度并控制多尺度特性。
HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations
- 引入带饱和控制的双曲正弦激活，显式调节梯度大小。
- 在图像、音频、视频、NeRF和SDF上均优于或媲美SIREN等方法。
- 提供超参数选择指南，适用于高保真隐式表示场景。
周期性激活函数（如正弦）通过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和多尺度行为控制不足的问题。本文提出双曲振荡器饱和控制（HOSC）激活函数，定义为 HOSC(x) = tanh(β sin(ω₀x))，其中参数β直接控制激活函数的Lipschitz界为βω₀，从而显式调节梯度幅度，同时保持周期性特征。我们提供了数学分析，并在图像、音频、视频、NeRF和SDF任务上，采用标准化训练协议进行了全面实证研究。与SIREN、FINER等方法的对比表明，HOSC在多个场景下取得显著优势，在其他场景也达到竞争性表现。结果验证了HOSC作为INR应用中实用周期激活的有效性，并给出了领域特定的超参数选择建议。代码可访问项目页 https://hosc-nn.github.io/。
原文摘要 · Abstract (English)
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/ .
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