  Previous studies have used a specific success metric within an algorithmic
search framework to prove machine learning impossibility results. However, this
specific success metric prevents us from applying these results on other forms
of machine learning, e.g. transfer learning. We define decomposable metrics as
a category of success metrics for search problems which can be expressed as a
linear operation on a probability distribution to solve this issue. Using an
arbitrary decomposable metric to measure the success of a search, we
demonstrate theorems which bound success in various ways, generalizing several
existing results in the literature.
