# Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification

arXiv: https://arxiv.org/abs/2101.03154 · HTML: https://mlsanity.com/paper/2101.03154/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 8 Jan 2021.

## Builds on (most cited first, 7 of 7)

- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [Tensor Networks for Medical Image Classification](https://mlsanity.com/paper/2004.10076/) (2020)
- [Needles in Haystacks: On Classifying Tiny Objects in Large Images](https://mlsanity.com/paper/1908.06037/) (2019)
- [Entanglement Entropy of Target Functions for Image Classification and Convolutional Neural Network](https://mlsanity.com/paper/1710.05520/) (2017)
- [Number-State Preserving Tensor Networks as Classifiers for Supervised Learning](https://mlsanity.com/paper/1905.06352/) (2019)

## Built on by (most cited first, 9 of 9)

- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [AQ-PINNs: Attention-Enhanced Quantum Physics-Informed Neural Networks for Carbon-Efficient Climate Modeling](https://mlsanity.com/paper/2409.01626/) (2024)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Quantum Artificial Intelligence for the Science of Climate Change](https://mlsanity.com/paper/2108.10855/) (2021)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)

## Abstract (arXiv)

Tiny object classification problem exists in many machine learning applications like medical imaging or remote sensing, where the object of interest usually occupies a small region of the whole image. It is challenging to design an efficient machine learning model with respect to tiny object of interest. Current neural network structures are unable to deal with tiny object efficiently because they are mainly developed for images featured by large scale objects. However, in quantum physics, there is a great theoretical foundation guiding us to analyze the target function for image classification regarding to specific objects size ratio. In our work, we apply Tensor Networks to solve this arising tough machine learning problem. First, we summarize the previous work that connects quantum spin model to image classification and bring the theory into the scenario of tiny object classification. Second, we propose using 2D multi-scale entanglement renormalization ansatz (MERA) to classify tiny objects in image. In the end, our experimental results indicate that tensor network models are effective for tiny object classification problem and potentially will beat state-of-the-art. Our codes will be available online https://github.com/timqqt/MERA_Image_Classification.