# TRIDENT: The Nonlinear Trilogy for Implicit Neural Representations

arXiv: https://arxiv.org/abs/2311.13610 · HTML: https://mlsanity.com/paper/2311.13610/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [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)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems](https://mlsanity.com/paper/2012.05703/) (2020)
- [NeuralGrasps: Learning Implicit Representations for Grasps of Multiple Robotic Hands](https://mlsanity.com/paper/2207.02959/) (2022)

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

- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Superpixel-informed Implicit Neural Representation for Multi-Dimensional Data](https://mlsanity.com/paper/2411.11356/) (2024)
- [H-SIREN: Improving implicit neural representations with hyperbolic periodic functions](https://mlsanity.com/paper/2410.04716/) (2024)

## Abstract (arXiv)

Implicit neural representations (INRs) have garnered significant interest recently for their ability to model complex, high-dimensional data without explicit parameterisation. In this work, we introduce TRIDENT, a novel function for implicit neural representations characterised by a trilogy of nonlinearities. Firstly, it is designed to represent high-order features through order compactness. Secondly, TRIDENT efficiently captures frequency information, a feature called frequency compactness. Thirdly, it has the capability to represent signals or images such that most of its energy is concentrated in a limited spatial region, denoting spatial compactness. We demonstrated through extensive experiments on various inverse problems that our proposed function outperforms existing implicit neural representation functions.