  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.
