Approximating Longer Birth and Death Processes with Large Language Models and the Self Improvement Framework

Birth and Death Processes are continuous-time Markov chains that transition to either the next or previous state. They model population sizes; state transitions lead to the births and deaths of individuals in a population. We model large,structured birth and death processes on large language models by simulating population data and training large language models to predict the next population. As large language models struggle with large and complicated inputs, we apply previously studied length generalization methods to the problem, including extending the self improvement framework to data from birth and death processes to benchmark performance. To overcome underfitting caused by low difficulty added per self improvement framework round, we parameterize the variance added by each self improvement round through the number of population states added. The Chapman-Kolmogorov equation shows us that the number of population states added each self improvement round influences the variance that the large language models fit to. Finally, we compare applied methods of length generalization in this domain. Our source code can be found on Github at https://anonymous.4open.science/r/self_improving_bd_processes/README.md.