Enlightening Artificial Intelligence with Science

Abstract

Today’s artifciail intelligence (AI) systems, while remarkably capable, are largely black boxes. The black-box nature raises concerns for those who build AI – “How can we construct an understand AI in scientifically grounded ways?”, and those who use AI – “How can we trust systems we do not understand?”. This thesis takes a humble step towards addressing the black-box problem. Building white boxes with science (Science for AI): The prevailing paradigm in AI today – “scaling is all you need" – focuses on scaling up existing models. However, this approach often yields systems that are neither interpretable nor efficient. I argue that scientific principles offer fresh perspectives for designing more transparent and effective AI systems. This is demonstrated through Kolmogorov-Arnold Networks (KANs) inspired by mathematics, Poisson Flow Generative Models (PFGM) rooted in physical intuition, and brain-inspired modular training (BIMT) drawing insights from neuroscience, etc. Opening black boxes (Science of AI): Modern AI models exhibit a range of puzzling behaviors – such as grokking, neural scaling laws and emergent representation learning – whose underlying mechanisms remain poorly understood. I employed simplified “spherical cow” models to investigate these phenomena from the perspective of phase transitions. I will show that grokking is a special phase in the hyperparameter space, which can be controlled and eliminated. The learned algorithms after grokking also display distinct phases, called clock or pizza algorithms. AI for Science: With greater interpretability, AI systems can begin to function as “AI Scientists” capable of (re)discovering deep scientific structures from data. These include conservation laws, hidden symmetries, integrable systems, Langrangian and Hamiltonian formulations, modular structures, and high-precion solutions. I believe my research work contributes to the emerging interdiscipinary field that unites AI and Science. Building opon the foundation laid in this thesis, I envision a future in which science guides AI out of its current era of alchemy and into a true era of scientific understanding.