If failure is defined as a model becoming unable to escape a non-global local minimum through training, it is almost guaranteed to occur with a non-trivial and finite training set. This can be attributed to inherent textbf{model identifiability} issues, which may allow uncountably infinite local minima to exist. In practice, however, experts believe that most relevant local minima are already close to the global minimum when given sufficiently large training sets, although this remains an active area of research.