Are there any fundamental limits on the ability of high-entropy initializations to overcome slow mixing in multimodal energy landscapes, or are there broader classes of models where such initializations can be shown to be universally effective
While high-entropy initializations offer a promising approach to overcoming slow mixing in multimodal energy landscapes, there may be fundamental limits to their effectiveness in certain scenarios. In highly complex energy landscapes with intricate topological features and multiple metastable states, the benefits of high-entropy initializations may be limited by the presence of deep energy minima and narrow transition regions. In such cases, the dynamics of the system may still get trapped in local optima or struggle to escape from metastable states, even with high-entropy initializations. However, for a broader class of models with well-separated energy basins and smoother energy landscapes, high-entropy initializations can be shown to be universally effective in promoting exploration and convergence. By carefully analyzing the structure of the energy landscape and the dynamics of the system, researchers can identify the regimes where high-entropy initializations provide significant advantages and where they may face limitations in facilitating efficient sampling and convergence.