This research provides theoretical foundations for why gradient orthogonalization techniques are significantly improving deep neural network training performance.

• Establishes that orthogonalized gradient methods function as first-order trust-region optimization with constraints based on matrix spectral norms
• Bridges the gap between empirical success and theoretical understanding of these optimization approaches
• Offers a mathematical framework for developing improved training algorithms

For engineering teams, this research enables more efficient and stable training of complex deep learning models by providing principled optimization techniques backed by rigorous mathematical analysis.

Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization