Recently, plugging trainable structural layers into deep convolutional neural networks (CNNs) as image representations has made promising progress. However, there has been little work on inserting parametric probability distributions, which can effectively model feature statistics, into deep CNNs in an end-to-end manner. This paper proposes a Global Gaussian Distribution embedding Network (G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DeNet) to take a step towards addressing this problem. The core of G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DeNet is a novel trainable layer of a global Gaussian as an image representation plugged into deep CNNs for end-to-end learning. The challenge is that the proposed layer involves Gaussian distributions whose space is not a linear space, which makes its forward and backward propagations be non-intuitive and non-trivial. To tackle this issue, we employ a Gaussian embedding strategy which respects the structures of both Riemannian manifold and smooth group of Gaussians. Based on this strategy, we construct the proposed global Gaussian embedding layer and decompose it into two sub-layers: the matrix partition sub-layer decoupling the mean vector and covariance matrix entangled in the embedding matrix, and the square-rooted, symmetric positive definite matrix sub-layer. In this way, we can derive the partial derivatives associated with the proposed structural layer and thus allow backpropagation of gradients. Experimental results on large scale region classification and fine-grained recognition tasks show that G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DeNet is superior to its counterparts, capable of achieving state-of-the-art performance.
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