  We show how a declarative functional programming specification of
backpropagation yields a visual and transparent implementation within
spreadsheets. We call our method Visual Backpropagation. This backpropagation
implementation exploits array worksheet formulas, manual calculation, and has a
sequential order of computation similar to the processing of a systolic array.
The implementation uses no hidden macros nor user-defined functions; there are
no loops, assignment statements, or links to any procedural programs written in
conventional languages. As an illustration, we compare a Visual Backpropagation
solution to a Tensorflow (Python) solution on a standard regression problem.
