A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.
核心贡献 · Key contributions
提出带有动态路由协议的 CapsNet，在 MNIST 上达到 0.25% 的测试错误率，为当时最优。 Introduces CapsNet with dynamic routing-by-agreement, achieving state-of-the-art 0.25% test error on MNIST.
胶囊使用向量输出表示实例化参数，向量长度表示实体存在概率。 Capsules use vector outputs to represent instantiation parameters, with vector length indicating entity existence.
动态路由实现了对高度重叠数字的优越分割，在 MultiMNIST 上优于 CNN。 Dynamic routing enables superior segmentation of highly overlapping digits, outperforming CNNs on MultiMNIST.
CapsNet 对仿射变换的泛化能力优于 CNN，在 affNIST 上达到 79% 对比 66%。 CapsNet generalizes better to affine transformations than CNNs, achieving 79% vs 66% on affNIST.
模型使用重构正则化强制姿态编码，提升了路由性能。 The model uses a reconstruction regularizer to enforce pose encoding, improving routing performance.
胶囊通过变换矩阵提供视角不变知识，避免了 CNN 的指数级低效问题。 Capsules provide viewpoint-invariant knowledge via transformation matrices, avoiding exponential inefficiencies of CNNs.
局限 · Limitations
假设每个位置最多存在一个胶囊实体，限制了处理同类别多个对象的能力。 Assumes at most one instance of a capsule's entity per location, limiting handling of multiple same-class objects.
在 CIFAR-10 上性能一般（10.6% 错误率），因为胶囊难以处理复杂背景。 Performance on CIFAR-10 (10.6% error) is modest, as capsules struggle with complex backgrounds.
模型较浅（3 层），可能难以扩展到更深架构或更大数据集。 The model is shallow (3 layers) and may not scale well to deeper architectures or larger datasets.
胶囊网络仍处于早期研究阶段，需要更多洞察才能超越 CNN 等成熟技术。 Capsule networks are still in early research stage, requiring more insights to outperform mature technologies like CNNs.
论文章节 · Sections（共 14）
摘要Abstract
1 引言1 Introduction
2 胶囊的向量输入和输出如何计算2 How the vector inputs and outputs of a capsule are computed
3 数字存在性的边际损失3 Margin loss for digit existence
4 CapsNet 架构4 CapsNet architecture
4.1 重建作为正则化方法4.1 Reconstruction as a regularization method
5 MNIST 上的胶囊网络5 Capsules on MNIST
5.1 胶囊各维度代表什么5.1 What the individual dimensions of a capsule represent
5.2 对仿射变换的鲁棒性5.2 Robustness to Affine Transformations