Richardson’s concept of arms race dynamics is considered, with two objectives in mind. One is to examine the degree to which hostility, prior levels of armaments and changes in those levels by rivals facilitate the prediction of current arms, with specific attention to year-by-year changes in the quantity of United States military personnel. The second objective is to begin to evaluate the use of artificial neural networks as a way to model learning, not only in arms races, but in a broad range of social phenomena. The results show that Richardson’s class of variables alone are insufficient to predict changes in U.S. military personnel. However, these variables do predict some major, seemingly discontinuous, shifts in military personnel that arise from demobilization following the end of war. Apparently, the neural network approach can learn to discern the end of war before any clear, overt action has taken place to signal it.