Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers

Researchers introduce a theoretical framework connecting Kolmogorov complexity to Transformer neural networks through asymptotically optimal description length objectives. The work demonstrates computational universality of Transformers and proposes a variational objective that achieves optimal compression, though current optimization methods struggle to find such solutions from random initialization.

• →The paper establishes theoretical foundations for applying Minimum Description Length principle to Transformer architectures using Kolmogorov complexity.
• →Researchers prove that asymptotically optimal description length objectives exist for Transformers by demonstrating their computational universality.
• →A tractable variational objective based on adaptive Gaussian mixture priors was constructed to achieve optimal compression guarantees.
• →Empirical tests show the method selects low-complexity solutions with strong generalization but faces optimization challenges with standard methods.
• →The framework provides a potential path toward training neural networks with better compression and generalization capabilities.