Principled Adaptive Loss Functions: An Information-Theoretic Framework for Dynamic Optimization in Deep Learning

Keywords: adaptive optimization, loss functions, information theory, meta-learning, deep learning, convergence analysis, training dynamics, optimization theory

Abstract: Deep neural network training relies on static loss function design, limiting performance on complex optimization landscapes. We introduce Principled Adaptive Loss Functions (PALF), a theoretically grounded framework that dynamically evolves loss functions based on information-theoretic principles and real-time training analysis. Our approach formulates loss adaptation as optimization in the space of loss functionals, guided by: (1) maximizing information flow between predictions and labels, (2) maintaining optimization stability through Lyapunov constraints, and (3) promoting generalization via complexity regularization. We provide convergence guarantees and demonstrate that PALF provably improves upon static functions. Experiments across 12 datasets show consistent improvements of 15-35% in performance, 40-60% faster convergence, and enhanced robustness. PALF discovers interpretable adaptation patterns that align with known optimization phases, providing new insights into deep network training dynamics.

Submission Number: 217