# Tensor Network for Supervised Learning at Finite Temperature

arXiv: https://arxiv.org/abs/2104.05439 · HTML: https://mlsanity.com/paper/2104.05439/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 9 Apr 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [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)
- [Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model](https://mlsanity.com/paper/1609.05587/) (2016)
- [TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks](https://mlsanity.com/paper/1905.01331/) (2019)
- [Bayesian Neural Networks at Finite Temperature](https://mlsanity.com/paper/1904.04154/) (2019)
- [Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning](https://mlsanity.com/paper/1907.10290/) (2019)

## Abstract (arXiv)

The large variation of datasets is a huge barrier for image classification tasks. In this paper, we embraced this observation and introduce the finite temperature tensor network (FTTN), which imports the thermal perturbation into the matrix product states framework by placing all images in an environment with constant temperature, in analog to energy-based learning. Tensor network is chosen since it is the best platform to introduce thermal fluctuation. Different from traditional network structure which directly takes the summation of individual losses as its loss function, FTTN regards it as thermal average loss computed from the entanglement with the environment. The temperature-like parameter can be automatically optimized, which gives each database an individual temperature. FTTN obtains improvement in both test accuracy and convergence speed in several datasets. The non-zero temperature automatically separates similar features, avoiding the wrong classification in previous architecture. The thermal fluctuation may give a better improvement in other frameworks, and we may also implement the temperature of database to improve the training effect.