  Despite the empirical success of knowledge distillation, current
state-of-the-art methods are computationally expensive to train, which makes
them difficult to adopt in practice. To address this problem, we introduce two
distinct complementary losses inspired by a cheap entropy-like estimator. These
losses aim to maximise the correlation and mutual information between the
student and teacher representations. Our method incurs significantly less
training overheads than other approaches and achieves competitive performance
to the state-of-the-art on the knowledge distillation and cross-model transfer
tasks. We further demonstrate the effectiveness of our method on a binary
distillation task, whereby it leads to a new state-of-the-art for binary
quantisation and approaches the performance of a full precision model. Code:
www.github.com/roymiles/ITRD
