# Position: Tensor Networks are a Valuable Asset for Green AI

arXiv: https://arxiv.org/abs/2205.12961 · HTML: https://mlsanity.com/paper/2205.12961/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 104 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Towards the Systematic Reporting of the Energy and Carbon Footprints of Machine Learning](https://mlsanity.com/paper/2002.05651/) (2020)
- [Sustainable AI: Environmental Implications, Challenges and Opportunities](https://mlsanity.com/paper/2111.00364/) (2021)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Predictability and Surprise in Large Generative Models](https://mlsanity.com/paper/2202.07785/) (2022)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [The Computational Limits of Deep Learning](https://mlsanity.com/paper/2007.05558/) (2020)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Hyperparameter Optimization: Foundations, Algorithms, Best Practices and Open Challenges](https://mlsanity.com/paper/2107.05847/) (2021)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [Chasing Carbon: The Elusive Environmental Footprint of Computing](https://mlsanity.com/paper/2011.02839/) (2020)
- [Tensor-Train Recurrent Neural Networks for Video Classification](https://mlsanity.com/paper/1707.01786/) (2017)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Measuring the Algorithmic Efficiency of Neural Networks](https://mlsanity.com/paper/2005.04305/) (2020)

## Built on by (most cited first, 3 of 3)

- [Certified Neural Approximations of Nonlinear Dynamics](https://mlsanity.com/paper/2505.15497/) (2025)
- [Unpacking the Implicit Norm Dynamics of Sharpness-Aware Minimization in Tensorized Models](https://mlsanity.com/paper/2508.10435/) (2025)
- [Adapting Tensor Kernel Machines to Enable Efficient Transfer Learning for Seizure Detection](https://mlsanity.com/paper/2512.02626/) (2025)

## Abstract (arXiv)

For the first time, this position paper introduces a fundamental link between tensor networks (TNs) and Green AI, highlighting their synergistic potential to enhance both the inclusivity and sustainability of AI research. We argue that TNs are valuable for Green AI due to their strong mathematical backbone and inherent logarithmic compression potential. We undertake a comprehensive review of the ongoing discussions on Green AI, emphasizing the importance of sustainability and inclusivity in AI research to demonstrate the significance of establishing the link between Green AI and TNs. To support our position, we first provide a comprehensive overview of efficiency metrics proposed in Green AI literature and then evaluate examples of TNs in the fields of kernel machines and deep learning using the proposed efficiency metrics. This position paper aims to incentivize meaningful, constructive discussions by bridging fundamental principles of Green AI and TNs. We advocate for researchers to seriously evaluate the integration of TNs into their research projects, and in alignment with the link established in this paper, we support prior calls encouraging researchers to treat Green AI principles as a research priority.