Algorithms and Hardness for Attention and Kernel Density Estimation

Explore the computational challenges and algorithmic solutions for Attention in Large Language Models and Kernel Density Estimation in this Google TechTalk presented by Josh Alman. Dive into the quadratic-time algorithms for both problems and discover recent advancements in achieving almost linear-time performance through techniques like the Fast Multipole Method and the polynomial method. Examine fine-grained hardness results that demonstrate the optimality of these approaches in specific parameter regimes, while identifying potential areas for improvement. Learn about the speaker's collaborative research efforts and gain insights into the intersection of algorithm design, complexity theory, and algebraic tools for enhancing algorithmic efficiency.