Deep neural networks allow for fusion of high-level features from multiple modalities and have become a promising end-to-end solution for multi-modal sensor fusion. While the recently proposed gating architectures improve the conventional fusion mechanisms employed in CNNs, these models are not always resilient particularly under the presence of sensor failures. This paper shows that the existing gating architectures fail to robustly learn the fusion weights that critically gate different modalities, leading to the issue of fusion weight inconsistency. We propose a new gating architecture by incorporating an auxiliary model to regularize the main model such that the fusion weight for each sensory modality can be robustly learned. As a result, this new auxiliary-model regulated architecture and its variants outperform the existing non-gating and gating fusion architectures under both clean and corrupted sensory inputs resulted from sensor failures. The obtained performance gains are rather significant in the latter case.

Numerically locating the critical points of non-convex surfaces is a long-standing problem central to many fields. Recently, the loss surfaces of deep neural networks have been explored to gain insight into outstanding questions in optimization, generalization, and network architecture design. However, the degree to which recently-proposed methods for numerically recovering critical points actually do so has not been thoroughly evaluated. In this paper, we examine this issue in a case for which the ground truth is known: the deep linear autoencoder. We investigate two sub-problems associated with numerical critical point identification: first, because of large parameter counts, it is infeasible to find all of the critical points for contemporary neural networks, necessitating sampling approaches whose characteristics are poorly understood; second, the numerical tolerance for accurately identifying a critical point is unknown, and conservative tolerances are difficult to satisfy. We first identify connections between recently-proposed methods and well-understood methods in other fields, including chemical physics, economics, and algebraic geometry. We find that several methods work well at recovering certain information about loss surfaces, but fail to take an unbiased sample of critical points. Furthermore, numerical tolerance must be very strict to ensure that numerically-identified critical points have similar properties to true analytical critical points. We also identify a recently-published Newton method for optimization that outperforms previous methods as a critical point-finding algorithm. We expect our results will guide future attempts to numerically study critical points in large nonlinear neural networks.

Motivation: Deep learning architectures have recently demonstrated their power in predicting DNA- and RNA-binding specificities. Existing methods fall into three classes: Some are based on Convolutional Neural Networks (CNNs), others use Recurrent Neural Networks (RNNs), and others rely on hybrid architectures combining CNNs and RNNs. However, based on existing studies it is still unclear which deep learning architecture is achieving the best performance. Thus an in-depth analysis and evaluation of the different methods is needed to fully evaluate their relative. Results: In this study, We present a systematic exploration of various deep learning architectures for predicting DNA- and RNA-binding specificities. For this purpose, we present deepRAM, an end-to-end deep learning tool that provides an implementation of novel and previously proposed architectures; its fully automatic model selection procedure allows us to perform a fair and unbiased comparison of deep learning architectures. We find that an architecture that uses k-mer embedding to represent the sequence, a convolutional layer and a recurrent layer, outperforms all other methods in terms of model accuracy. Our work provides guidelines that will assist the practitioner in choosing the best architecture for the task at hand, and provides some insights on the differences between the models learned by convolutional and recurrent networks. In particular, we find that although recurrent networks improve model accuracy, this comes at the expense of a loss in the interpretability of the features learned by the model. Availability and implementation: The source code for deepRAM is available at https://github.com/MedChaabane/deepRAM

This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the dataset consists of signals defined on many different graphs, and the learned filters should generalize to signals on new graphs, not present in the training set. A necessary condition for transferability (the ability to transfer filters) is stability. Namely, given a graph filter, if we add a small perturbation to the graph, then the filter on the perturbed graph is a small perturbation of the original filter. It is a common misconception that spectral filters are not stable, and this paper aims at debunking this mistake. We introduce a space of filters, called the Cayley smoothness space, that contains the filters of state-of-the-art spectral filtering methods, and whose filters can approximate any generic spectral filter. For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable. By combining stability with the known property of equivariance, we prove that graph spectral filters are transferable.

Many machine learning tasks require sampling a subset of items from a collection. Due to the non-differentiability of subset sampling, the procedure is usually not included in end-to-end deep learning models. We show that through a connection to weighted reservoir sampling, the Gumbel-max trick can be extended to produce exact subset samples, and that a recently proposed top-k relaxation can be used to differentiate through the subset sampling procedure. We test our method on end-to-end tasks requiring subset sampling, including a differentiable k-nearest neighbors task and an instance-wise feature selection task for model interpretability.

The article proposes a new framework for assessment of physical rehabilitation exercises based on a deep learning approach. The objective of the framework is automated quantification of patient performance in completing prescribed rehabilitation exercises, based on captured whole-body joint trajectories. The main components of the framework are metrics for measuring movement performance, scoring functions for mapping the performance metrics into numerical scores of movement quality, and deep neural network models for regressing quality scores of input movements via supervised learning. Furthermore, an overview of the existing methods for modeling and evaluation of rehabilitation movements is presented, encompassing various distance functions, dimensionality-reduction techniques, and movement models employed for this problem in prior studies. To the best of our knowledge, this is the first work that implements deep neural network for assessment of rehabilitation performance. Multiple deep network architectures are repurposed for the task in hand and are validated on a dataset of rehabilitation exercises.

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a model-based approach, whereas, geometric matrix completion models combine the best from both approaches. Existing deep-learning-based geometric models yield good performance, but, in order to operate, they require a fixed structure graph capturing the relationships among the users and items. This graph is typically constructed by evaluating a pre-defined similarity metric on the available observations or by using side information, e.g., user profiles. In contrast, Markov-random-fields-based models do not require a fixed structure graph but rely on handcrafted features to make predictions. When no side information is available and the number of available observations becomes very low, existing solutions are pushed to their limits. In this paper, we propose a geometric matrix completion approach that addresses these challenges. We consider matrix completion as a structured prediction problem in a conditional random field (CRF), which is characterized by a maximum a posterior (MAP) inference, and we propose a deep model that predicts the missing entries by solving the MAP inference problem. The proposed model simultaneously learns the similarities among matrix entries, computes the CRF potentials, and solves the inference problem. Its training is performed in an end-to-end manner, with a method to supervise the learning of entry similarities. Comprehensive experiments demonstrate the superior performance of the proposed model compared to various state-of-the-art models on popular benchmark datasets and underline its superior capacity to deal with highly incomplete matrices.

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore, can be to used to design robust DNNs. In this work, this problem is studied through the lens of compression which is captured by the low-rank structure of weight matrices. It is first shown that adversarial training tends to promote simultaneously low-rank and sparse structure in the weight matrices of neural networks. This is measured through the notions of effective rank and effective sparsity. In the reverse direction, when the low rank structure is promoted by nuclear norm regularization and combined with sparsity inducing regularizations, neural networks show significantly improved adversarial robustness. The effect of nuclear norm regularization on adversarial robustness is paramount when it is applied to convolutional neural networks. Although still not competing with adversarial training, this result contributes to understanding the key properties of robust classifiers.

We describe techniques for training high-quality image denoising models that require only single instances of corrupted images as training data. Inspired by a recent technique that removes the need for supervision through image pairs by employing networks with a "blind spot" in the receptive field, we address two of its shortcomings: inefficient training and somewhat disappointing final denoising performance. This is achieved through a novel blind-spot convolutional network architecture that allows efficient self-supervised training, as well as application of Bayesian distribution prediction on output colors. Together, they bring the self-supervised model on par with fully supervised deep learning techniques in terms of both quality and training speed in the case of i.i.d. Gaussian noise.

In this paper, we study deep fully circulant neural networks, that is deep neural networks in which all weight matrices are circulant ones. We show that these networks outperform the recently introduced deep networks with other types of structured layers. Besides introducing principled techniques for training these models, we provide theoretical guarantees regarding their expressivity. Indeed, we prove that the function space spanned by circulant networks of bounded depth includes the one spanned by dense networks with specific properties on their rank. We conduct a thorough experimental study to compare the performance of deep fully circulant networks with state of the art models based on structured matrices and with dense models. We show that our models achieve better accuracy than their structured alternatives while required 2x fewer weights as the next best approach. Finally we train deep fully circulant networks to build a compact and accurate models on a real world video classification dataset with over 3.8 million training examples.