Generalizations of Matrix Multiplication for Solving the Light Bulb Problem

Explore a groundbreaking approach to solving the Light Bulb Problem in this conference talk from the Workshop on Tensors: Quantum Information, Complexity and Combinatorics. Delve into the history of this 30-year-old problem introduced by L. Valiant and its applications in data analysis, statistics, and learning theory. Examine the limitations of traditional algorithms and the breakthrough achieved by G. Valiant in 2012 using fast matrix multiplication. Learn about a novel method that replaces matrix multiplication with similar tensors of potentially lower rank, potentially leading to faster computation. Discover how a 4*4*4 tensor with rank 5 can outperform Strassen's algorithm when applied to previous approaches. Gain insights into the speaker's optimism for this new technique and understand the broader implications of using alternative tensors for solving various algorithmic problems beyond matrix multiplication.