In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data. In this work, we study the setting where the data (or measurements) are ordered, longitudinal or temporal in nature and live on a Riemannian manifold -- this setting is common in a variety of problems in statistical machine learning, vision and medical imaging. We show how statistical recurrent network models can be defined in such spaces. We give an efficient algorithm and conduct a rigorous analysis of its statistical properties. We perform extensive numerical experiments showing competitive performance with state of the art methods but with far fewer parameters. We also show applications to a statistical analysis task in brain imaging, a regime where deep neural network models have only been utilized in limited ways.

Image classification has become one of the main tasks in the field of computer vision technologies. In this context, a recent algorithm called CapsNet that implements an approach based on activity vectors and dynamic routing between capsules may overcome some of the limitations of the current state of the art artificial neural networks (ANN) classifiers, such as convolutional neural networks (CNN). In this paper, we evaluated the performance of the CapsNet algorithm in comparison with three well-known classifiers (Fisher-faces, LeNet, and ResNet). We tested the classification accuracy on four datasets with a different number of instances and classes, including images of faces, traffic signs, and everyday objects. The evaluation results show that even for simple architectures, training the CapsNet algorithm requires significant computational resources and its classification performance falls below the average accuracy values of the other three classifiers. However, we argue that CapsNet seems to be a promising new technique for image classification, and further experiments using more robust computation resources and re-fined CapsNet architectures may produce better outcomes.

Supervised machine learning based state-of-the-art computer vision techniques are in general data hungry and pose the challenges of not having adequate computing resources and of high costs involved in human labeling efforts. Training data subset selection and active learning techniques have been proposed as possible solutions to these challenges respectively. A special class of subset selection functions naturally model notions of diversity, coverage and representation and they can be used to eliminate redundancy and thus lend themselves well for training data subset selection. They can also help improve the efficiency of active learning in further reducing human labeling efforts by selecting a subset of the examples obtained using the conventional uncertainty sampling based techniques. In this work we empirically demonstrate the effectiveness of two diversity models, namely the Facility-Location and Disparity-Min models for training-data subset selection and reducing labeling effort. We do this for a variety of computer vision tasks including Gender Recognition, Scene Recognition and Object Recognition. Our results show that subset selection done in the right way can add 2-3% in accuracy on existing baselines, particularly in the case of less training data. This allows the training of complex machine learning models (like Convolutional Neural Networks) with much less training data while incurring minimal performance loss.

Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generated via reparameterization. Not only does SIVI expand the variational family to incorporate highly flexible variational distributions, including implicit ones that have no analytic density functions, but also sandwiches the evidence lower bound (ELBO) between a lower bound and an upper bound, and further derives an asymptotically exact surrogate ELBO that is amenable to optimization via stochastic gradient ascent. With a substantially expanded variational family and a novel optimization algorithm, SIVI is shown to closely match the accuracy of MCMC in inferring the posterior in a variety of Bayesian inference tasks.

For humans, the process of grasping an object relies heavily on rich tactile feedback. Recent robotic grasping work, however, has been largely based only on visual input, and thus cannot easily benefit from feedback after initiating contact. In this paper, we investigate if a robot can learn to use tactile information to iteratively and efficiently adjust its grasp. To this end, we propose an end-to-end action-conditional model that learns greedy regrasping policies from raw visuo-tactile data. This model - a deep, multimodal convolutional network - predicts the outcome of a candidate grasp adjustment, and then executes a grasp by iteratively selecting the most promising actions. Our approach requires neither calibration of the tactile sensors, nor any analytical modeling of contact forces, thus reducing the engineering effort required to obtain efficient grasping policies. We train our model with data from over 6,450 grasping trials on a two-finger gripper equipped with GelSight high-resolution tactile sensors on each finger. Across extensive experiments, our approach outperforms a variety of baselines at (i) estimating grasp adjustment outcomes, (ii) selecting efficient grasp adjustments for quick grasping, and (iii) reducing the amount of force applied at the fingers, while maintaining competitive performance. Finally, we study the choices made by our model and show that it has successfully acquired useful and interpretable grasping behaviors.

We propose and study the problem of distribution-preserving lossy compression. Motivated by the recent advances in extreme image compression which allow to maintain artifact-free reconstructions even at very low bitrates, we propose to optimize the rate-distortion tradeoff under the constraint that the reconstructed samples follow the distribution of the training data. Such a compression system recovers both ends of the spectrum: On one hand, at zero bitrate it learns a generative model of the data, and at high enough bitrates it achieves perfect reconstruction. Furthermore, for intermediate bitrates it smoothly interpolates between matching the distribution of the training data and perfectly reconstructing the training samples. We study several methods to approximately solve the proposed optimization problem, including a novel combination of Wasserstein GAN and Wasserstein Autoencoder, and present strong theoretical and empirical results for the proposed compression system.

We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with the original Helmholtz machine and later variational autoencoder algorithms (but unlike adverserial methods) our approach learns an explicit inference or "recognition" model to approximate the posterior distribution over the latent variables. Unlike in these earlier methods, the posterior representation is not limited to a narrow tractable parameterised form (nor is it represented by samples). To train the generative and recognition models we develop an extended wake-sleep algorithm inspired by the original Helmholtz Machine. This makes it possible to learn hierarchical latent models with both discrete and continuous variables, where an accurate posterior representation is essential. We demonstrate that the new algorithm outperforms current state-of-the-art methods on synthetic, natural image patch and the MNIST data sets.

We study the tradeoff between computational effort and accuracy in a cascade of deep neural networks. During inference, early termination in the cascade is controlled by confidence levels derived directly from the softmax outputs of intermediate classifiers. The advantage of early termination is that classification is performed using less computation, thus adjusting the computational effort to the complexity of the input. Moreover, dynamic modification of confidence thresholds allow one to trade accuracy for computational effort without requiring retraining. Basing of early termination on softmax classifier outputs is justified by experimentation that demonstrates an almost linear relation between confidence levels in intermediate classifiers and accuracy. Our experimentation with architectures based on ResNet obtained the following results.

Deep Neural Networks have been applied very successfully in image recognition and natural language processing. Recently these powerful methods have received attention also in the brain-computer interface (BCI) community. Here, we introduce a convolutional neural network (CNN) architecture optimized for classification of brain states from non-invasive magnetoencephalographic (MEG) measurements. The model structure is motivated by a state-of-the-art generative model of the MEG signal and is thus readily interpretable in neurophysiological terms. We demonstrate that the proposed model is highly accurate in decoding event-related responses as well as modulations of oscillatory brain activity, and is robust with respect to inter-individual differences. Importantly, the model generalizes well across users: when trained on data pooled from previous users, it can successfully perform on new users. Thus, the time-consuming BCI calibration can be omitted. Moreover, the model can be incrementally updated, resulting in +8.9% average accuracy improvement in offline experiments and +17.0% in a real-time BCI. We argue that this model can be used in practical BCIs and basic neuroscience research.

Deep neural networks made a striking entree in machine learning and quickly became state-of-the-art algorithms in many tasks such as computer vision [1, 2, 3, 4], speech recognition and generation [5, 6] or natural language processing [7, 8]. However, deep neural networks are known for being very sensitive to their input, and adversarial examples provide a good illustration of their lack of robustness [9, 10]. Indeed, a well-chosen small perturbation of the input image can mislead a neural network and significantly decrease its classification accuracy. One metric to assess the robustness of neural networks to small perturbations is the Lipschitz constant (see Definition 1), which upper bounds the relationship between input perturbation and output variation for a given distance. For generative models, the recent Wasserstein GAN [11] improved the training stability of GANs by reformulating the optimization problem as a minimization of the Wasserstein distance between the real and generated distributions [12]. However, this method relies on an efficient way of constraining the Lipschitz constant of the critic, which was only partially addressed in the original paper, and the object of several followup works [13, 14]. Recently, the Lipschitz continuity was used in order to improve the state-of-the-art in several deep 1 learning topics: (1) for robust learning, avoiding adversarial attacks was achieved in [15] by constraining local Lipschitz constants in neural networks.