In this thesis, we present a simple and effective architecture called Bilinear Convolutional Neural Networks (B-CNNs). These networks represent an image as a pooled outer product of features derived from two CNNs and capture localized feature interactions in a translationally invariant manner. B-CNNs generalize classical orderless texture-based image models such as bag-of-visual-words and Fisher vector representations. However, unlike prior work, they can be trained in an end-to-end manner. In the experiments, we demonstrate that these representations generalize well to novel domains by fine-tuning and achieve excellent results on fine-grained, texture and scene recognition tasks. The visualization of fine-tuned convolutional filters shows that the models are able to capture highly localized attributes. We present a texture synthesis framework that allows us to visualize the pre-images of fine-grained categories and the invariances that are captured by these models.
In order to enhance the discriminative power of the B-CNN representations, we investigate normalization techniques for rescaling the importance of individual features during aggregation. Spectral normalization scales the spectrum of the covariance matrix obtained after bilinear pooling and offers a significant improvement. However, the computation involves singular value decomposition, which is not computationally efficient on modern GPUs. We present an iteration-based approximation of matrix square-root along with its gradients to speed up the computation and study its effect on fine-tuning deep neural networks. Another approach is democratic aggregation, which aims to equalize the contributions of individual feature vector into the final pooled image descriptor. This achieves a comparable improvement, and can be approximated in a low-dimensional embedding unlike the spectral normalization. Therefore, this approach is friendly to aggregating higher-dimensional features. We demonstrate that the two approaches are closely related, and we discuss their trade-off between performance and efficiency
