With the promising progress of deep neural networks, layer aggregation has been used to fuse information across layers in various fields, such as computer vision and machine translation. However, most of the previous methods combine layers in a static fashion in that their aggregation strategy is independent of specific hidden states. Inspired by recent progress on capsule networks, in this paper we propose to use routing-by-agreement strategies to aggregate layers dynamically. Specifically, the algorithm learns the probability of a part (individual layer representations) assigned to a whole (aggregated representations) in an iterative way and combines parts accordingly. We implement our algorithm on top of the state-of-the-art neural machine translation model TRANSFORMER and conduct experiments on the widely-used WMT14 English-German and WMT17 Chinese-English translation datasets. Experimental results across language pairs show that the proposed approach consistently outperforms the strong baseline model and a representative static aggregation model.
The idea of dynamic routing is first proposed by Sabour:2017:NIPS , which aims at addressing the representational limitations of convolutional and recurrent neural networks for image classification. The iterative routing procedure is further improved by using Expectation-Maximization algorithm to better estimate the agreement between capsules @cite_28 . In computer vision community, xi2017capsule explore its application on CIFAR data with higher dimensionality. lalonde2018capsules apply capsule networks on object segmentation task.
@cite_28
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A capsule is a group of neurons whose outputs represent different properties of the same entity. Each layer in a capsule network contains many capsules [a group of capsules forms a capsule layer and can be used in place of a traditional layer in a neural net]. We describe a version of capsules in which each capsule has a logistic unit to represent the presence of an entity and a 4x4 matrix which could learn to represent the relationship between that entity and the viewer (the pose). A capsule in one layer votes for the pose matrix of many different capsules in the layer above by multiplying its own pose matrix by trainable viewpoint-invariant transformation matrices that could learn to represent part-whole relationships. Each of these votes is weighted by an assignment coefficient. These coefficients are iteratively updated for each image using the Expectation-Maximization algorithm such that the output of each capsule is routed to a capsule in the layer above that receives a cluster of similar votes. The transformation matrices are trained discriminatively by backpropagating through the unrolled iterations of EM between each pair of adjacent capsule layers. On the smallNORB benchmark, capsules reduce the number of test errors by 45 compared to the state-of-the-art. Capsules also show far more resistance to white box adversarial attack than our baseline convolutional neural network.