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Research on sample complexity focuses on determining the minimum number of data points needed to accurately solve various machine learning and statistical problems. Current efforts concentrate on improving sample efficiency for tasks like tensor completion, Gaussian mixture modeling, and high-dimensional regression, often employing techniques like coresets, score matching, and best-of-n sampling to reduce the required data. These advancements are crucial for improving the scalability and efficiency of algorithms, particularly in high-dimensional settings and resource-constrained environments, impacting fields ranging from quantum computing to federated learning. The development of tighter theoretical bounds and efficient algorithms directly translates to practical improvements in data analysis and machine learning applications.