Despite rapid progress in state-of-the-art AI models for theoretical physics, most such methods remain black boxes: lacking guarantees of robust and reliable predictions that meet uncertainty quantification benchmarks essential in scientific domains. To address this gap, I will present a few directions that improve robustness, mechanistic interpretability, and uncertainty quantification of complex learning and sample generation abilities, by combining quantum and statistical field theories with computational statistics. First, I will present the simplest model capable of in-context learning, an ability that underpins Large Language Model (LLM) success, particularly for quantum. Leveraging Replica Mean Field Theory and Random Matrix Theory, the performance of a simplified LLM is exactly derived in the joint asymptotic limit of a large number of training samples, token dimensions, sample length, and task diversity: exhibiting a phase transition in learning abilities. Next, I will introduce Neural Network Field Theory Correspondence, a paradigm which generates field theory samples without any training algorithms, while guaranteeing low uncertainty bounds at scale. This explainable + interpretable alternative to Monte Carlo sampling facilitates a bidirectional mapping between field theory actions and their dual Neural Network architectures. Lastly, I will present a framework for systematic coarsegraining of data features irrelevant to learning objectives. Building on the Renormalization Group (RG), this scheme ensures that perturbations to model predictions caused by such coarsegraining are bound within scientific uncertainty measures, while capturing nontrivial corrections elusive to the state-of-the-art spectral bias method. Altogether, these Physics-of-AI approaches advance Scientific AI reliability in a first-principles manner, while bridging AI with fundamental physics.
Zoom link: https://zoom.us/j/92666778187?pwd=ck75MvO4b54m78HHKBxYnIeFBEG5pG.1
