Differentiable Matrix

Differentiable matrices are matrices whose elements can be treated as variables within a differentiable function, enabling their use in gradient-based optimization algorithms. Current research focuses on developing efficient algorithms for computing matrix operations like square roots and inverses differentiably, often employing techniques like Taylor polynomials, Padé approximants, and iterative methods to improve computational speed. This capability is proving valuable across diverse fields, including machine learning (e.g., self-supervised learning and improved neural network architectures), robotics and computer vision (e.g., optimization in structured learning), and high-energy physics (e.g., enabling differentiable simulations). The development of efficient and accurate differentiable matrix operations is thus significantly advancing several scientific and engineering disciplines.