# Tensor Network Estimation of Distribution Algorithms

arXiv: https://arxiv.org/abs/2412.19780 · HTML: https://mlsanity.com/paper/2412.19780/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 59 references that are in the map.
- First posted on arXiv 27 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [Evolving Deep Neural Networks](https://mlsanity.com/paper/1703.00548/) (2017)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Bias and Generalization in Deep Generative Models: An Empirical Study](https://mlsanity.com/paper/1811.03259/) (2018)
- [Evolving Mario Levels in the Latent Space of a Deep Convolutional Generative Adversarial Network](https://mlsanity.com/paper/1805.00728/) (2018)
- [Surrogate NAS Benchmarks: Going Beyond the Limited Search Spaces of Tabular NAS Benchmarks](https://mlsanity.com/paper/2008.09777/) (2020)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [CMA-ES for Hyperparameter Optimization of Deep Neural Networks](https://mlsanity.com/paper/1604.07269/) (2016)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)
- [Quantum Tensor Networks, Stochastic Processes, and Weighted Automata](https://mlsanity.com/paper/2010.10653/) (2020)
- [Generalization Metrics for Practical Quantum Advantage in Generative Models](https://mlsanity.com/paper/2201.08770/) (2022)
- [Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework](https://mlsanity.com/paper/2106.15666/) (2021)
- [Generative Adversarial Networks in Estimation of Distribution Algorithms for Combinatorial Optimization](https://mlsanity.com/paper/1509.09235/) (2015)
- [Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints](https://mlsanity.com/paper/2405.09005/) (2024)

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

- [Tensor Cookbook: Mastering Tensors through Diagrams](https://mlsanity.com/paper/2605.16610/) (2026)

## Abstract (arXiv)

Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into evolutionary optimization algorithms have appeared in the recent literature. In essence, these methods can be understood as replacing the traditional crossover operation of a genetic algorithm with a tensor network-based generative model. We investigate these methods from the point of view that they are Estimation of Distribution Algorithms (EDAs). We find that optimization performance of these methods is not related to the power of the generative model in a straightforward way. Generative models that are better (in the sense that they better model the distribution from which their training data is drawn) do not necessarily result in better performance of the optimization algorithm they form a part of. This raises the question of how best to incorporate powerful generative models into optimization routines. In light of this we find that adding an explicit mutation operator to the output of the generative model often improves optimization performance.