  Mean squared error (MSE) is one of the most widely used metrics to expression
differences between multi-dimensional entities, including images. However, MSE
is not locally sensitive as it does not take into account the spatial
arrangement of the (pixel) differences, which matters for structured data types
like images. Such spatial arrangements carry information about the source of
the differences; therefore, an error function that also incorporates the
location of errors can lead to a more meaningful distance measure. We introduce
Proximally Sensitive Error (PSE), through which we suggest that a regional
emphasis in the error measure can 'highlight' semantic differences between
images over syntactic/random deviations. We demonstrate that this emphasis can
be leveraged upon for the task of anomaly/occlusion detection. We further
explore its utility as a loss function to help a model focus on learning
representations of semantic objects instead of minimizing syntactic
reconstruction noise.
