Computational Complexity

Computational complexity studies the inherent difficulty of computational problems, aiming to classify problems based on their resource requirements (time, memory). Current research focuses on analyzing the complexity of algorithms for tasks like large language model training and inference, manifold learning (e.g., diffusion maps), and solving optimization problems arising in machine learning (e.g., finding stationary points in non-convex optimization). Understanding these complexities is crucial for designing efficient algorithms and for establishing fundamental limits on what can be computed, impacting fields ranging from artificial intelligence to algorithm design and theoretical computer science.