# Comb Tensor Networks vs. Matrix Product States: Enhanced Efficiency in High-Dimensional Spaces

arXiv: https://arxiv.org/abs/2412.06857 · HTML: https://mlsanity.com/paper/2412.06857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 8 Dec 2024.

## Builds on (most cited first, 1 of 1)

- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)

## Abstract (arXiv)

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product States (MPS) architectures. Here, we demonstrate that beyond a certain threshold in data and bond dimensions, a comb-shaped tensor network architecture can yield more efficient contractions than a standard MPS. This finding suggests that for continuous and high-dimensional data distributions, transitioning from MPS to a comb tensor network representation can substantially reduce computational overhead while maintaining accuracy.