# Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions

arXiv: https://arxiv.org/abs/2608.17135 · HTML: https://mlsanity.com/paper/2608.17135/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 51 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 3 of 3)

- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Free-Energy Machine for Combinatorial Optimization](https://mlsanity.com/paper/2412.09285/) (2024)

## Abstract (arXiv)

Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to 270 configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.