Complexity dynamics of learning systems

Thesis

We study complexity and generalization in learning systems. We begin by framing learning as a dynamical non-equilibrium process, and suggest that a more complete understanding of machine learning requires methods beyond statistical description. We point out that machine learning must be considered both a mathematical and a natural science, since it requires both a theory of the formal learning system and the environment it operates within. Our central technical contribution is a dynamical complexity measure based on the theory of Kolmogorov complexity and lossy compression. We use this measure to demonstrate a complexity phase transition during learning, in neural networks which suddenly generalize after initially overfitting their training data. We also explore generalization in multi-step decision processes, which break common statistical assumptions underlying generalization. Finally, we explore generalization of learning systems trained only in simulation to the real world.

Authors: Demoss, B

• DOI: 10.5287/ora-o5q9580kp
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: complex systems; world models; machine learning; reinforcement learning; imitation learning; algorithmic information theory
• Subjects: Machine Learning