# Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA

arXiv: https://arxiv.org/abs/2507.09091 · HTML: https://mlsanity.com/paper/2507.09091/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 12 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [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)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Point Cloud Audio Processing](https://mlsanity.com/paper/2105.02469/) (2021)
- [Rethinking Non-Negative Matrix Factorization with Implicit Neural Representations](https://mlsanity.com/paper/2404.04439/) (2024)

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

- [Learning Orthonormal Bases for Function Spaces](https://mlsanity.com/paper/2605.19959/) (2026)

## Abstract (arXiv)

We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to learn numerical approximations to solve the problem. Modeling signals as continuous-time stochastic processes, we unify the approaches to both the PCA and ICA problems in the continuous setting through a contrast function term in the network loss, enforcing the desired statistical properties of the source signals (decorrelation, independence) learned in the decomposition. This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals where standard techniques are not applicable.