  We present backpropagation clipping, a novel variant of differentially
private stochastic gradient descent (DP-SGD) for privacy-preserving deep
learning. Our approach clips each trainable layer's inputs (during the forward
pass) and its upstream gradients (during the backward pass) to ensure bounded
global sensitivity for the layer's gradient; this combination replaces the
gradient clipping step in existing DP-SGD variants. Our approach is simple to
implement in existing deep learning frameworks. The results of our empirical
evaluation demonstrate that backpropagation clipping provides higher accuracy
at lower values for the privacy parameter $\epsilon$ compared to previous work.
We achieve 98.7% accuracy for MNIST with $\epsilon = 0.07$ and 74% accuracy for
CIFAR-10 with $\epsilon = 3.64$.
