The field of tensor networks and low-rank modeling is witnessing significant advancements, driven by the need for efficient and accurate representations of high-dimensional data. Researchers are exploring innovative approaches to improve the predictive power and computational efficiency of tensor network models, particularly in applications such as chaotic time series prediction and hyperspectral anomaly detection. A key trend is the integration of domain knowledge and large language models to inform the structure of tensor networks, enabling more accurate and interpretable representations. Additionally, low-rank modeling techniques are being enhanced through the development of novel modules that facilitate information flow across low-rank subspaces, leading to improved performance and reduced parameter requirements. Notable papers include:

• A tensor network approach that demonstrates improved accuracy and computational efficiency in chaotic time series prediction.
• A hyperspectral anomaly detection method that leverages unified nonconvex tensor ring factors regularization to capture spatial-spectral correlations.
• A low-rank training module that boosts the performance of foundation models through latent crossing.
• A domain-aware tensor network structure search framework that utilizes large language models to predict suitable tensor network structures.