The field of tensor-based methods for data representation and analysis is rapidly advancing, with a focus on developing innovative techniques for low-rank tensor decomposition, robust tensor completion, and uncertain mode surface analysis. Recent work has explored the use of neural networks and machine learning algorithms to improve the accuracy and efficiency of these methods. Notably, the integration of tensor decomposition with techniques such as meta-learning and clustered implicit neural representations has shown promising results in encoding complex scientific simulation data. Furthermore, the development of new loss functions and regularization techniques has enhanced the robustness of tensor-based methods to outliers and noise. Overall, these advancements have significant implications for various applications, including image and video processing, traffic data estimation, and materials science. Noteworthy papers in this area include: The paper on Low-Rank Implicit Neural Representation via Schatten-p Quasi-Norm and Jacobian Regularization, which proposes a novel approach to low-rank tensor representation using neural networks. The paper on MC-INR: Efficient Encoding of Multivariate Scientific Simulation Data using Meta-Learning and Clustered Implicit Neural Representations, which introduces a framework for encoding multivariate data on unstructured grids using meta-learning and clustering. The paper on Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations, which develops a class of approximately equivariant networks for machine learning interatomic potentials using low-rank tensor decompositions.