Later, an instanton liquid model was studied. This model starts from the assumption that an ensemble of instantons cannot be described by a mere sum of separate instantons. Various models have been proposed, introducing interactions between instantons or using variational methods (like the "valley approximation") endeavoring to approximate the exact multi-instanton solution as closely as possible. Many phenomenological successes have been reached. Whether an instanton liquid can explain confinement in 3+1 dimensional QCD is not known, but many physicists think that it is unlikely.