  We address the challenging problem of deep representation learning--the
efficient adaption of a pre-trained deep network to different tasks.
Specifically, we propose to explore gradient-based features. These features are
gradients of the model parameters with respect to a task-specific loss given an
input sample. Our key innovation is the design of a linear model that
incorporates both gradient and activation of the pre-trained network. We show
that our model provides a local linear approximation to an underlying deep
model, and discuss important theoretical insights. Moreover, we present an
efficient algorithm for the training and inference of our model without
computing the actual gradient. Our method is evaluated across a number of
representation-learning tasks on several datasets and using different network
architectures. Strong results are obtained in all settings, and are
well-aligned with our theoretical insights.
