  We provide a detailed exposition of the connections between Boltzmann
machines commonly utilized in machine learning problems and the ideas already
well known in quantum statistical mechanics through Feynman's description of
the same. We find that this equivalence allows the interpretation that the
hidden layers in Boltzmann machines and other neural network formalisms are in
fact discrete versions of path elements that are present within the Feynman
path-integral formalism. Since Feynman paths are the natural and elegant
depiction of interference phenomena germane to quantum mechanics, it appears
that in machine learning, the goal is to find an appropriate combination of
``paths'', along with accumulated path-weights, through a network that
cumulatively capture the correct $x \rightarrow y$ map for a given mathematical
problem. As a direct consequence of this analysis, we are able to provide
general quantum circuit models that are applicable to both Boltzmann machines
and to Feynman path integral descriptions. Connections are also made to inverse
quantum scattering problems which allow a robust way to define
``interpretable'' hidden layers.
