3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the last layer of a network. Instead, an idealized model would preserve a meaningful representation of the voxelized object, while explaining the pose-difference between the two inputs. An equivariant representation vector has two components: the invariant identity part, and a discernable encoding of the transformation. Models that can’t explain pose-differences risk “diluting” the representation, in pursuit of optimizing a classification or regression loss function.
There are many papers which also focus on learning equivariance. Tangent Prop by Simard al @cite_5 is a classic example of an invariance inducing regularizer. Hinton al @cite_34 introduced the transforming autoencoder to build latent spaces with equivariant structure. More recently, Worrall al @cite_17 extended this method by imposing explicit transformation rules on the latent space. Papers such as InfoGAN by Chen al @cite_30 and the Deep Convolutional Inverse Graphics Network of Kulkarni al @cite_46 seek to learn equivariant structure in unsupervised fashion unsupervised. Most recently Sabour al @cite_9 and Hinton al @cite_2 achieved highly impressive results on the MNIST dataset with capsule networks by learning approximations to affine equivariance. While these methods are very flexible, they require lots of training data
@cite_30 @cite_9 @cite_2 @cite_5 @cite_46 @cite_34 @cite_17
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This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that also maximizes the mutual information between a small subset of the latent variables and the observation. We derive a lower bound to the mutual information objective that can be optimized efficiently, and show that our training procedure can be interpreted as a variation of the Wake-Sleep algorithm. Specifically, InfoGAN successfully disentangles writing styles from digit shapes on the MNIST dataset, pose from lighting of 3D rendered images, and background digits from the central digit on the SVHN dataset. It also discovers visual concepts that include hair styles, presence absence of eyeglasses, and emotions on the CelebA face dataset. Experiments show that InfoGAN learns interpretable representations that are competitive with representations learned by existing fully supervised methods. 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. 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. In many machine learning applications, one has access, not only to training data, but also to some high-level a priori knowledge about the desired behavior of the system. For example, it is known in advance that the output of a character recognizer should be invariant with respect to small spatial distortions of the input images (translations, rotations, scale changes, etcetera). We have implemented a scheme that allows a network to learn the derivative of its outputs with respect to distortion operators of our choosing. This not only reduces the learning time and the amount of training data, but also provides a powerful language for specifying what generalizations we wish the network to perform. This paper presents the Deep Convolution Inverse Graphics Network (DC-IGN), a model that aims to learn an interpretable representation of images, disentangled with respect to three-dimensional scene structure and viewing transformations such as depth rotations and lighting variations. The DC-IGN model is composed of multiple layers of convolution and de-convolution operators and is trained using the Stochastic Gradient Variational Bayes (SGVB) algorithm [10]. We propose a training procedure to encourage neurons in the graphics code layer to represent a specific transformation (e.g. pose or light). Given a single input image, our model can generate new images of the same object with variations in pose and lighting. We present qualitative and quantitative tests of the model's efficacy at learning a 3D rendering engine for varied object classes including faces and chairs. Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the relative feature space relationship between two rotated images? What is decoded when we interpolate in feature space? Ideally, we want to disentangle confounding factors, such as pose, appearance, and illumination, from object identity. Disentangling these is difficult because they interact in very nonlinear ways. We propose a simple method to construct a deep feature space, with explicitly disentangled representations of several known transformations. A person or algorithm can then manipulate the disentangled representation, for example, to re-render an image with explicit control over parameterized degrees of freedom. The feature space is constructed using a transforming encoder-decoder network with a custom feature transform layer, acting on the hidden representations. We demonstrate the advantages of explicit disentangling on a variety of datasets and transformations, and as an aid for traditional tasks, such as classification.