  When humans learn a new concept, they might ignore examples that they cannot
make sense of at first, and only later focus on such examples, when they are
more useful for learning. We propose incorporating this idea of tunable
sensitivity for hard examples in neural network learning, using a new
generalization of the cross-entropy gradient step, which can be used in place
of the gradient in any gradient-based training method. The generalized gradient
is parameterized by a value that controls the sensitivity of the training
process to harder training examples. We tested our method on several benchmark
datasets. We propose, and corroborate in our experiments, that the optimal
level of sensitivity to hard example is positively correlated with the depth of
the network. Moreover, the test prediction error obtained by our method is
generally lower than that of the vanilla cross-entropy gradient learner. We
therefore conclude that tunable sensitivity can be helpful for neural network
learning.
