Linear Subspace
Linear subspaces are fundamental mathematical structures used to represent lower-dimensional representations of higher-dimensional data, aiming to capture essential information while reducing complexity. Current research focuses on developing algorithms to learn and utilize these subspaces within various machine learning models, including variational autoencoders and large language models, often employing techniques like singular value decomposition and Riemannian optimization. This work has significant implications for improving model generalization, stability, and efficiency across diverse applications such as system control, image processing, and natural language processing, particularly in scenarios with high-dimensional data or limited training samples.