The self-attention mechanisms play a crucial role in multiple applications, for example modern large language models (LLMs), but their growing adoption has led to rapidly increasing energy, water, economic, and hardware demands. This thesis examines the application of the Primal-Dual Kernel Multi-linear Singular Value Decomposition (KMLSVD) framework as introduced by Wesel and Batselier on the self-attention mechanism. The Primal-Dual KMLSVD attention framework makes three-dimensional self-attention possible enabling a more information rich representation, possibly increasing accuracy, computation time and/or a decrease in energy and hardware requirements. Furthermore, the Primal formulation does not compute the attention tensor, significantly decreasing the computational and time complexity. Therefore, Primal-Dual KMLSVD attention could play a major role in green AI applications. Three tests are performed on 10 different timeseries datasets in order to: i) find the most accurate Primal KMLSVD attention variant, ii) compare Primal to Dual KMLSVD attention and iii) compare the Primal-Dual KMLSVD attention framework to primal attention and canonical attention. The results of these tests prove that Primal-Dual KMLSVD can define self-attention in 3D but, as of writing this thesis, the current used formulations are too inefficient time wise to be a valid improvement or alternative to self-attention. Furthermore, small scale tests suggest that Primal-Dual KMLSVD might not even be required to define self attention in 3D. However, as no experiments were performed on higher-order (3D) datasets, the potential of this framework for such problems remains an open question.