  We reduce training time in convolutional networks (CNNs) with a method that,
for some of the mini-batches: a) scales down the resolution of input images via
downsampling, and b) reduces the forward pass operations via pooling on the
convolution filters. Training is performed in an interleaved fashion; some
batches undergo the regular forward and backpropagation passes with original
network parameters, whereas others undergo a forward pass with pooled filters
and downsampled inputs. Since pooling is differentiable, the gradients of the
pooled filters propagate to the original network parameters for a standard
parameter update. The latter phase requires fewer floating point operations and
less storage due to the reduced spatial dimensions in feature maps and filters.
The key idea is that this phase leads to smaller and approximate updates and
thus slower learning, but at significantly reduced cost, followed by passes
that use the original network parameters as a refinement stage. Deciding how
often and for which batches the downsmapling occurs can be done either
stochastically or deterministically, and can be defined as a training
hyperparameter itself. Experiments on residual architectures show that we can
achieve up to 23% reduction in training time with minimal loss in validation
accuracy.
