  We describe Fibres of Failure (FiFa), a method to classify failure modes of
predictive processes using the Mapper algorithm from Topological Data Analysis.
  Our method uses Mapper to build a graph model of input data stratified by
prediction error.
  Groupings found in high-error regions of the Mapper model then provide
distinct failure modes of the predictive process.
  We demonstrate FiFa on misclassifications of MNIST images with added noise,
and demonstrate two ways to use the failure mode classification: either to
produce a correction layer that adjusts predictions by similarity to the
failure modes; or to inspect members of the failure modes to illustrate and
investigate what characterizes each failure mode.
