  We propose to explain the predictions of a deep neural network, by pointing
to the set of what we call representer points in the training set, for a given
test point prediction. Specifically, we show that we can decompose the
pre-activation prediction of a neural network into a linear combination of
activations of training points, with the weights corresponding to what we call
representer values, which thus capture the importance of that training point on
the learned parameters of the network. But it provides a deeper understanding
of the network than simply training point influence: with positive representer
values corresponding to excitatory training points, and negative values
corresponding to inhibitory points, which as we show provides considerably more
insight. Our method is also much more scalable, allowing for real-time feedback
in a manner not feasible with influence functions.
