# COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations

arXiv: https://arxiv.org/abs/2505.11640 · HTML: https://mlsanity.com/paper/2505.11640/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 19 of 19)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (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)
- [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)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [FoV-NeRF: Foveated Neural Radiance Fields for Virtual Reality](https://mlsanity.com/paper/2103.16365/) (2021)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [A Sampling Theory Perspective on Activations for Implicit Neural Representations](https://mlsanity.com/paper/2402.05427/) (2024)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [HOSC: A Periodic Activation Function for Preserving Sharp Features in Implicit Neural Representations](https://mlsanity.com/paper/2401.10967/) (2024)

## Built on by (most cited first, 1 of 1)

- [Implicit Neural Representations: A Signal Processing Perspective](https://mlsanity.com/paper/2604.15047/) (2026)

## Abstract (arXiv)

Implicit neural representations (INRs) are a powerful paradigm for modeling data, offering a continuous alternative to discrete signal representations. Their ability to compactly encode complex signals has led to strong performance in many vision tasks. Prior work shows INR performance is highly sensitive to the choice of activation function in the underlying multilayer perceptron, yet the theoretical reasons remain unclear. Key limitations also persist, including spectral bias (reduced sensitivity to high-frequency content), limited robustness to noise, and difficulty capturing local and global structure jointly. We analyze INR signal representation using harmonic analysis and Chebyshev polynomials. We prove that modulating activation functions with a complex sinusoidal term yields richer and more complete spectral support throughout the network. Building on this, we introduce a new activation function tailored to INRs and validate our theory using Chebyshev analysis and extensive experiments. We additionally use a regularized deep prior, extracted from a task-specific model, to adapt the activations, further improving convergence speed and stability. Across image reconstruction (average PSNR gain of +5.67 dB over the nearest counterpart on a diverse dataset), denoising (+0.46 dB PSNR), super-resolution (+0.64 dB over the nearest SOTA method for 6X upscaling), inpainting, and 3D shape reconstruction, our activation consistently outperforms existing state-of-the-art alternatives.