Sparse Function

Sparse function learning focuses on efficiently identifying and utilizing the most relevant features from high-dimensional data, aiming to overcome the "curse of dimensionality." Current research emphasizes developing algorithms and theoretical frameworks for learning sparse representations using various approaches, including gradient descent methods, $\ell_1$ minimization, and randomized algorithms tailored to specific architectures like neural networks (particularly transformers and two-layer networks). This research is crucial for improving the efficiency and scalability of machine learning models across diverse applications, from robot navigation and high-dimensional PDE solving to model compression and reinforcement learning.