A Geometrically-Grounded Drive for MDL-Based Optimization in Deep Learning

Researchers introduce a novel optimization framework that integrates the Minimum Description Length (MDL) principle directly into deep neural network training dynamics. The method uses geometrically-grounded cognitive manifolds with coupled Ricci flow to create autonomous model simplification while maintaining data fidelity, with theoretical guarantees for convergence and practical O(N log N) complexity.

• →Novel framework transforms MDL from a model selection tool into an active optimization driver for deep learning training.
• →Uses geometrically-grounded cognitive manifolds with coupled Ricci flow and MDL Drive term for autonomous model compression.
• →Provides theoretical guarantees including monotonic description length decrease and finite topological phase transitions.
• →Achieves computationally efficient O(N log N) per-iteration complexity with numerical stability guarantees.
• →Empirical validation shows improved generalization and autonomous model simplification on synthetic tasks.