  Second-order pooling, a.k.a.~bilinear pooling, has proven effective for deep
learning based visual recognition. However, the resulting second-order networks
yield a final representation that is orders of magnitude larger than that of
standard, first-order ones, making them memory-intensive and cumbersome to
deploy. Here, we introduce a general, parametric compression strategy that can
produce more compact representations than existing compression techniques, yet
outperform both compressed and uncompressed second-order models. Our approach
is motivated by a statistical analysis of the network's activations, relying on
operations that lead to a Gaussian-distributed final representation, as
inherently used by first-order deep networks. As evidenced by our experiments,
this lets us outperform the state-of-the-art first-order and second-order
models on several benchmark recognition datasets.
