The effect of the temperature parameter on convergence in the Boltzmann machines

Boltzmann machines show attractive features in traditional neural network tasks. We tested the robustness of the Boltzmann machine in a non-linear mapping task. The system's errors were classified into several categories and the distribution of errors between the categories was studied. Using simulations, it is demonstrated that limitation of the temperature parameter causes the distribution of the network's errors to be unique and different from its usual error distribution. The phenomenon receives a mathematical explanation rooted in the statistical mechanics basics of the Boltzmann machine. This has applications in designing and evaluating mapping tasks for the Boltzmann machines and can help speed up system convergence, which is known to be a major deficit of the Boltzmann machine.