Adam Byerly

Adam Byerly, Tatiana Kalganova

We provide a definition for class density that can be used to measure the aggregate similarity of the samples within each of the classes in a high-dimensional, unstructured dataset. We then put forth several candidate methods for calculating class density and analyze the correlation between the values each method produces with the corresponding individual class test accuracies achieved on a trained model. Additionally, we propose a definition for dataset quality for high-dimensional, unstructured data and show that those datasets that met a certain quality threshold (experimentally demonstrated to be > 10 for the datasets studied) were candidates for eliding redundant data based on the individual class densities.

Adam Byerly, Tatiana Kalganova

We show that, for each of five datasets of increasing complexity, certain training samples are more informative of class membership than others. These samples can be identified a priori to training by analyzing their position in reduced dimensional space relative to the classes' centroids. Specifically, we demonstrate that samples nearer the classes' centroids are less informative than those that are furthest from it. For all five datasets, we show that there is no statistically significant difference between training on the entire training set and when excluding up to 2% of the data nearest to each class's centroid.

Adam Byerly, Tatiana Kalganova, Anthony J. Grichnik

We present a dataset consisting of high-resolution images of 13 micro-PCBs captured in various rotations and perspectives relative to the camera, with each sample labeled for PCB type, rotation category, and perspective categories. We then present the design and results of experimentation on combinations of rotations and perspectives used during training and the resulting impact on test accuracy. We then show when and how well data augmentation techniques are capable of simulating rotations vs. perspectives not present in the training data. We perform all experiments using CNNs with and without homogeneous vector capsules (HVCs) and investigate and show the capsules' ability to better encode the equivariance of the sub-components of the micro-PCBs. The results of our experiments lead us to conclude that training a neural network equipped with HVCs, capable of modeling equivariance among sub-components, coupled with training on a diversity of perspectives, achieves the greatest classification accuracy on micro-PCB data.

Adam Byerly, Tatiana Kalganova, Ian Dear

Most capsule network designs rely on traditional matrix multiplication between capsule layers and computationally expensive routing mechanisms to deal with the capsule dimensional entanglement that the matrix multiplication introduces. By using Homogeneous Vector Capsules (HVCs), which use element-wise multiplication rather than matrix multiplication, the dimensions of the capsules remain unentangled. In this work, we study HVCs as applied to the highly structured MNIST dataset in order to produce a direct comparison to the capsule research direction of Geoffrey Hinton, et al. In our study, we show that a simple convolutional neural network using HVCs performs as well as the prior best performing capsule network on MNIST using 5.5x fewer parameters, 4x fewer training epochs, no reconstruction sub-network, and requiring no routing mechanism. The addition of multiple classification branches to the network establishes a new state of the art for the MNIST dataset with an accuracy of 99.87% for an ensemble of these models, as well as establishing a new state of the art for a single model (99.83% accurate).

Adam Byerly, Tatiana Kalganova

Capsules are the name given by Geoffrey Hinton to vector-valued neurons. Neural networks traditionally produce a scalar value for an activated neuron. Capsules, on the other hand, produce a vector of values, which Hinton argues 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. First, a very simple monolithic CNN that when using HVCs achieved a 63% improvement in top-1 classification accuracy and a 35% improvement in top-5 classification accuracy over the baseline architecture. Second, with the CNN architecture referred to as Inception v3 that achieved similar accuracies both with and without HVCs. Additionally, the simple monolithic CNN when using HVCs showed no overfitting after more than 300 epochs whereas the baseline showed overfitting after 30 epochs. We use the ImageNet ILSVRC 2012 classification challenge dataset with both networks.