HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations

TL;DR

HOSC introduces a new periodic activation function with controllable gradient stability, enhancing high-fidelity implicit neural representations across various data modalities.

Contribution

The paper proposes HOSC, a novel periodic activation with explicit gradient control, and provides theoretical analysis and extensive empirical validation for INRs.

Findings

HOSC effectively controls gradient magnitudes via the parameter 2

HOSC achieves competitive performance with existing methods like SIREN and FINER

Domain-specific guidance improves hyperparameter tuning for HOSC

Abstract

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, $\text{HOSC}(x) = \tanh\bigl(\beta \sin(\omega_0 x)\bigr)$, which exposes an explicit parameter $\beta$ that controls the Lipschitz bound of the activation by $\beta \omega_0$. 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/ .