Max Fieg

Angelo Rajendram, Xieting Chu, Vijay Ganesh et al.

We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density estimation tasks has largely been unexplored. To address the SymDE task we introduce a multi-stage pipeline: (i) problem decomposition through clustering and/or probabilistic graphical model structure learning; (ii) nonparametric density estimation; (iii) support estimation; and finally (iv) SR on the density estimate. We demonstrate the efficacy of AI-Kolmogorov on synthetic mixture models, multivariate normal distributions, and three exotic distributions, two of which are motivated by applications in high-energy physics. We show that AI-Kolmogorov can discover underlying distributions or otherwise provide valuable insight into the mathematical expressions describing them.

Jason Benjamin Baretz, Max Fieg, Vijay Ganesh et al.

Particle physics theories, such as those which explain neutrino flavor mixing, arise from a vast landscape of model-building possibilities. A model's construction typically relies on the intuition of theorists. It also requires considerable effort to identify appropriate symmetry groups, assign field representations, and extract predictions for comparison with experimental data. We develop an Autonomous Model Builder (AMBer), a framework in which a reinforcement learning agent interacts with a streamlined physics software pipeline to search these spaces efficiently. AMBer selects symmetry groups, particle content, and group representation assignments to construct viable models while minimizing the number of free parameters introduced. We validate our approach in well-studied regions of theory space and extend the exploration to a novel, previously unexamined symmetry group. While demonstrated in the context of neutrino flavor theories, this approach of reinforcement learning with physics software feedback may be extended to other theoretical model-building problems in the future.