Homogeneous Vector Capsules Enable Adaptive Gradient Descent in Convolutional Neural Networks

Neural networks traditionally produce a scalar value for an activated neuron. Capsules, on the other hand, produce a vector of values, which has been shown to correspond to a single, composite feature wherein the values of the components of the vectors indicate properties of the feature such as transformation or contrast. We present a new way of parameterizing and training capsules that we refer to as homogeneous vector capsules (HVCs). We demonstrate, experimentally, that altering a convolutional neural network (CNN) to use HVCs can achieve superior classification accuracy without increasing the number of parameters or operations in its architecture as compared to a CNN using a single final fully connected layer. Additionally, the introduction of HVCs enables the use of adaptive gradient descent, reducing the dependence a model's achievable accuracy has on the finely tuned hyperparameters of a non-adaptive optimizer. We demonstrate our method and results using two neural network architectures. For the CNN architecture referred to as Inception v3, replacing the fully connected layers with HVCs increased the test accuracy by an average of 1.32% across all experiments conducted. For a simple monolithic CNN, we show HVCs improve test accuracy by an average of 19.16%.