# tn4ml: Tensor Network Training and Customization for Machine Learning

arXiv: https://arxiv.org/abs/2502.13090 · HTML: https://mlsanity.com/paper/2502.13090/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [Tensor networks for unsupervised machine learning](https://mlsanity.com/paper/2106.12974/) (2021)
- [Entanglement and Tensor Networks for Supervised Image Classification](https://mlsanity.com/paper/2007.06082/) (2020)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Tensor Networks for Explainable Machine Learning in Cybersecurity](https://mlsanity.com/paper/2401.00867/) (2023)
- [Tensor Regression Networks with various Low-Rank Tensor Approximations](https://mlsanity.com/paper/1712.09520/) (2017)
- [Tangent-Space Gradient Optimization of Tensor Network for Machine Learning](https://mlsanity.com/paper/2001.04029/) (2020)
- [tntorch: Tensor Network Learning with PyTorch](https://mlsanity.com/paper/2206.11128/) (2022)
- [TensorKrowch: Smooth integration of tensor networks in machine learning](https://mlsanity.com/paper/2306.08595/) (2023)

## Built on by (most cited first, 5 of 5)

- [Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC](https://mlsanity.com/paper/2506.00102/) (2025)
- [Towards Tensor Network Models for Low-Latency Jet Tagging on FPGAs](https://mlsanity.com/paper/2601.10801/) (2026)
- [Hardware-Aware Tensor Networks for Real-Time Quantum-Inspired Anomaly Detection at Particle Colliders](https://mlsanity.com/paper/2603.26604/) (2026)
- [Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability](https://mlsanity.com/paper/2608.30505/) (2026)
- [Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification](https://mlsanity.com/paper/2608.07043/) (2026)

## Abstract (arXiv)

Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.