The recent developments in the research area of tensor-based representations and their applications have shown significant advancements in both theoretical frameworks and practical implementations. A notable trend is the shift towards continuous and compositional representations that align more closely with the inherent continuity of deep learning vector spaces, addressing the limitations of traditional symbolic approaches. This has led to improved performance in tasks such as visual representation learning and hyperspectral image analysis. Additionally, there is a growing interest in extending tensor analysis to multidimensional quaternion data, providing new computational tools and theoretical foundations for handling complex multiway data. Randomized algorithms for low-rank approximation in tensor networks have also been introduced, offering efficient solutions for streamable tensor approximation. Furthermore, novel tensor network architectures, such as comb tensor networks, are being explored to enhance efficiency in high-dimensional spaces, outperforming traditional methods like Matrix Product States. These innovations collectively push the boundaries of tensor-based methods, making them more versatile and powerful across various domains.

Noteworthy papers include one proposing a continuous compositional representation framework that significantly improves disentanglement and convergence in visual representation learning, and another introducing a multilinear framework for quaternion tensors, offering new theoretical insights and computational tools for quaternion multiway data.