Fig. 2: Extracting symbolic relations from static distributions.
From: AI-assisted discovery of quantitative and formal models in social science
a Discovering the network densification process in paper citations. The top diagrams show the evolution of the arXiv high energy physics citation network over time. OccamNet is able to discover the correct functional form for the densification law axβ based on a table of network properties (Leskovec and Krevl, 2014). b A similar experiment is performed to discover the scaling law in the rank-size distribution of node degrees in the arXiv citation and Wikipedia hyperlink networks. At the same level of complexity regularization, OccamNet picks the simplest solution for each dataset, demonstrating the principle of Occam’s razor. Our model finds a power law for the Wikipedia network and a more complex function for the citation network. c We apply OccamNet to real-world, multi-dimensional economic data from Cobb and Douglas’s 1928 paper. The complexity-accuracy trade-off is evaluated by sweeping across the available modes of regularization.
