# Decoupling multivariate functions using a nonparametric filtered tensor decomposition

arXiv: https://arxiv.org/abs/2205.11153 · HTML: https://mlsanity.com/paper/2205.11153/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 10 of 10)

- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (2021)
- [Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling](https://mlsanity.com/paper/2001.02861/) (2020)
- [Grey-box state-space identification of nonlinear mechanical vibrations](https://mlsanity.com/paper/1804.10758/) (2018)
- [Decoupling multivariate functions using a non-parametric Filtered CPD approach](https://mlsanity.com/paper/2105.08518/) (2021)
- [Decoupling P-NARX models using filtered CPD](https://mlsanity.com/paper/2105.08530/) (2021)
- [PNLSS Toolbox 1.0](https://mlsanity.com/paper/2105.08534/) (2021)
- [Applying Polynomial Decoupling Methods to the Polynomial NARX Model](https://mlsanity.com/paper/2202.12423/) (2022)

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

- [Robust Basis Spline Decoupling for the Compression of Transformer Models](https://mlsanity.com/paper/2605.18794/) (2026)

## Abstract (arXiv)

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to interpret, in part because of the large number of required parameters. Decoupling techniques aim at providing an alternative representation of the nonlinearity. The so-called decoupled form is often a more efficient parameterisation of the relationship while being highly structured, favouring interpretability. In this work two new algorithms, based on filtered tensor decompositions of first order derivative information are introduced. The method returns nonparametric estimates of smooth decoupled functions. Direct applications are found in, i.a. the fields of nonlinear system identification and machine learning.