# FM-SIREN & FM-FINER: Implicit Neural Representation Using Nyquist-based Orthogonality

arXiv: https://arxiv.org/abs/2509.23438 · HTML: https://mlsanity.com/paper/2509.23438/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (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)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPs](https://mlsanity.com/paper/2111.15135/) (2021)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)

## Built on by (most cited first, 2 of 2)

- [Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation](https://mlsanity.com/paper/2606.06671/) (2026)
- [FiRe: Frequency Reparameterization as a Preconditioner for Periodic Implicit Neural Representations](https://mlsanity.com/paper/2606.29414/) (2026)

## Abstract (arXiv)

Existing periodic activation-based implicit neural representation (INR) networks, such as SIREN and FINER, suffer from hidden feature redundancy, where neurons within a layer capture overlapping frequency components due to the use of a fixed frequency multiplier. This redundancy limits the expressive capacity of multilayer perceptrons (MLPs). Drawing inspiration from classical signal processing methods such as the Discrete Sine Transform (DST), in this paper, we propose FM-SIREN and FM-FINER, which assign Nyquist-informed, neuron-specific frequency multipliers to periodic activations. Contrary to existing approaches, our design introduces frequency diversity without requiring hyperparameter tuning or additional network depth. This simple yet principled approach reduces the redundancy of features by nearly 50% and consistently improves signal reconstruction across diverse INR tasks, such as fitting 1D audio, 2D image and 3D shape, and video, outperforming their baseline counterparts while maintaining efficiency.