Natural gradient descent (NGD) is a powerful optimization technique for machine learning, but the computational complexity of the inverse Fisher information matrix limits its application in training deep neural networks. To overcome this challenge, we propose a novel optimization method for training deep neural networks called structured natural gradient descent (SNGD). Theoretically, we demonstrate that optimizing the original network using NGD is equivalent to using fast gradient descent (GD) to optimize the reconstructed network with a structural transformation of the parameter matrix. Thereby, we decompose the calculation of the global Fisher information matrix into the efficient computation of local Fisher matrices via constructing local Fisher layers in the reconstructed network to speed up the training. Experimental results on various deep networks and datasets demonstrate that SNGD achieves faster convergence speed than NGD while retaining comparable solutions. Furthermore, our method outperforms traditional GDs in terms of efficiency and effectiveness. Thus, our proposed method has the potential to significantly improve the scalability and efficiency of NGD in deep learning applications. Our source code is available at https://github.com/Chaochao-Lin/SNGD.

As massively parallel computations have become broadly available with modern GPUs, deep architectures trained on very large datasets have risen in popularity. Discriminatively trained convolutional neural networks, in particular, were recently shown to yield state-of-the-art performance in challenging image classification benchmarks such as ImageNet. However, elements of these architectures are similar to standard hand-crafted representations used in computer vision. In this paper, we explore the extent of this analogy, proposing a version of the stateof-the-art Fisher vector image encoding that can be stacked in multiple layers. This architecture significantly improves on standard Fisher vectors, and obtains competitive results with deep convolutional networks at a smaller computational learning cost. Our hybrid architecture allows us to assess how the performance of a conventional hand-crafted image classification pipeline changes with increased depth. We also show that convolutional networks and Fisher vector encodings are complementary in the sense that their combination further improves the accuracy.

As massively parallel computations have become broadly available with modern GPUs, deep architectures trained on very large datasets have risen in popularity. Discriminativelytrained convolutional neural networks, in particular, were recently shown to yield state-of-the-art performance in challenging image classification benchmarkssuch as ImageNet. However, elements of these architectures are similar to standard handcrafted representations used in computer vision. In this paper, we explore the extent of this analogy, proposing a version of the stateof-the-art Fishervector image encoding that can be stacked in multiple layers. This architecture significantly improves on standard Fisher vectors, and obtains competitive results with deep convolutional networks at a smaller computational learning cost. Our hybrid architecture allows us to assess how the performance of a conventional handcrafted image classification pipeline changes with increased depth. We also show that convolutional networks and Fisher vector encodings are complementary in the sense that their combination further improves the accuracy.