# SASNet: Spatially-Adaptive Sinusoidal Networks for INRs

arXiv: https://arxiv.org/abs/2503.09750 · HTML: https://mlsanity.com/paper/2503.09750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 30 of 36)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [Arbitrary-Scale Image Generation and Upsampling using Latent Diffusion Model and Implicit Neural Decoder](https://mlsanity.com/paper/2403.10255/) (2024)
- [A Sampling Theory Perspective on Activations for Implicit Neural Representations](https://mlsanity.com/paper/2402.05427/) (2024)
- [A Multi-Implicit Neural Representation for Fonts](https://mlsanity.com/paper/2106.06866/) (2021)
- [MINER: Multiscale Implicit Neural Representations](https://mlsanity.com/paper/2202.03532/) (2022)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [Neural Implicit Surface Evolution](https://mlsanity.com/paper/2201.09636/) (2022)
- [Neural Implicit Morphing of Face Images](https://mlsanity.com/paper/2308.13888/) (2023)

## Built on by (most cited first, 3 of 3)

- [Calibrated Harmonic Overlaid Implicit Neural Representations for Multi-Dimensional Data](https://mlsanity.com/paper/2606.26763/) (2026)
- [Towards High-Fidelity Gaussian Splatting with Queried-Convolution Neural Networks](https://mlsanity.com/paper/2512.12898/) (2025)
- [FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representations](https://mlsanity.com/paper/2606.29414/) (2026)

## Abstract (arXiv)

Sinusoidal neural networks (SIRENs) are powerful implicit neural representations (INRs) for low-dimensional signals in vision and graphics. By encoding input coordinates with sinusoidal functions, they enable high-frequency image and surface reconstruction. However, training SIRENs is often unstable and highly sensitive to frequency initialization: small frequencies produce overly smooth reconstructions in detailed regions, whereas large ones introduce spurious high-frequency components that manifest as noise in smooth areas such as image backgrounds. To address these challenges, we propose SASNet, a Spatially-Adaptive Sinusoidal Network that couples a frozen frequency embedding layer, which explicitly fixes the network's frequency support, with jointly learned spatial masks that localize neuron influence across the domain. This pairing stabilizes optimization, sharpens edges, and suppresses noise in smooth areas. Experiments on 2D image and 3D volumetric data fitting as well as signed distance field (SDF) reconstruction benchmarks demonstrate that SASNet achieves faster convergence, superior reconstruction quality, and robust frequency localization -- assigning low- and high-frequency neurons to smooth and detailed regions respectively -- while maintaining parameter efficiency. Code available here: https://github.com/Fengyee/SASNet_inr.