# Entangled q-Convolutional Neural Nets

arXiv: https://arxiv.org/abs/2103.11785 · HTML: https://mlsanity.com/paper/2103.11785/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 6 Mar 2021.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Inductive Bias of Deep Convolutional Networks through Pooling Geometry](https://mlsanity.com/paper/1605.06743/) (2016)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [Convolutional Rectifier Networks as Generalized Tensor Decompositions](https://mlsanity.com/paper/1603.00162/) (2016)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [Equivalence of restricted Boltzmann machines and tensor network states](https://mlsanity.com/paper/1701.04831/) (2017)
- [Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Design](https://mlsanity.com/paper/1704.01552/) (2017)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [Deep SimNets](https://mlsanity.com/paper/1506.03059/) (2015)
- [Tensor network language model](https://mlsanity.com/paper/1710.10248/) (2017)
- [Quantum Deformed Neural Networks](https://mlsanity.com/paper/2010.11189/) (2020)

## Built on by (most cited first, 4 of 4)

- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [ATP: Adaptive Threshold Pruning for Efficient Data Encoding in Quantum Neural Networks](https://mlsanity.com/paper/2503.21815/) (2025)
- [Tensor network to learn the wavefunction of data](https://mlsanity.com/paper/2111.08014/) (2021)
- [What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement](https://mlsanity.com/paper/2303.11249/) (2023)

## Abstract (arXiv)

We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We explain how the network associates a quantum state to each classification label, and study the entanglement structure of these network states. In both our experiments on the MNIST and Fashion-MNIST datasets, we observe a distinct increase in both the left/right as well as the up/down bipartition entanglement entropy during training as the network learns the fine features of the data. More generally, we observe a universal negative correlation between the value of the entanglement entropy and the value of the cost function, suggesting that the network needs to learn the entanglement structure in order the perform the task accurately. This supports the possibility of exploiting the entanglement structure as a guide to design the machine learning algorithm suitable for given tasks.