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

arXiv 2601.07870 ↗First posted 10 Jan 2026cs.LG cs.CV cs.GRcited by 0

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Abstract (arXiv)

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, HOSC(x) = tanhbigl(β sin(ω0 x)bigr), which exposes an explicit parameter β that controls the Lipschitz bound of the activation by β ω0. 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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References · 25

  1. 2022Instant Neural Graphics Primitives with a Multiresolution Hash Encodingcited by 3,723
  2. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  3. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  5. 2021Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fieldscited by 2,032
  6. 2021Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fieldscited by 1,964
  7. 2018On the Spectral Bias of Neural Networkscited by 1,341
  8. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  9. 2021NeRV: Neural Representations for Videoscited by 256
  10. 2021COIN: COmpression with Implicit Neural representationscited by 233
  11. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  12. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 174
13 more
  1. 2021BACON: Band-limited Coordinate Networks for Multiscale Scene Representationcited by 143
  2. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  3. 2021Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPscited by 135
  4. 2022GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimationcited by 86
  5. 2023Neural Point Catacaustics for Novel-View Synthesis of Reflectionscited by 82
  6. 2023FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functionscited by 78
  7. 2022Residual Multiplicative Filter Networks for Multiscale Reconstructioncited by 25
  8. 2024A Sampling Theory Perspective on Activations for Implicit Neural Representationscited by 24
  9. 2023Anti-Aliased Neural Implicit Surfaces with Encoding Level of Detailcited by 23
  10. 2021Periodic Activation Functions Induce Stationaritycited by 21
  11. 2024FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representationcited by 11
  12. 2024Neural Gaussian Scale-Space Fieldscited by 6
  13. 2025INR-Bench: A Unified Benchmark for Implicit Neural Representations in Multi-Domain Regression and Reconstructioncited by 1

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