Information Theory views learning as universal prediction under log loss, characterized through regret bounds. We propose a framework that provides non-uniform, model dependent bounds utilizing an effective notion of architecture-based model complexity. This complexity is defined by the probability mass or volume of the set of all models in the vicinity of the target model \theta_0, in an informational distance. This volume might be hard to evaluate, yet by local analysis it is related to spectral properties of the expected Hessian or the Fisher Information Matrix at \theta_0, leading to tractable approximations. We argue that successful architectures possess abroad complexity range, enabling learning in highly over-parameterized model classes. The framework sheds light on the role of inductive biases, the effectiveness of the stochastic gradient descent (SGD)algorithm (but also other algorithms), and phenomena such as flat minima. It unifies online, batch, supervised, and generative settings, and applies across the stochastic-realizable and agnostic regimes. Moreover, it provides insights into the success of modern machine-learning architectures, such as deep neural networks and transformers, suggesting that their broad complexity range naturally arises from their layered structure. These insights open the door to the design of alternative architectures with potentially comparable or even superior performance.
