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Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

Our theoretical understanding of deep learning has not kept pace with its empirical success. While network architecture is known to be critical, we do not yet understand its effect on learned representations and network behavior, or how…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Algorithms based on deep network models are being used for many pattern recognition and decision-making tasks in robotics and AI. Training these models requires a large labeled dataset and considerable computational resources, which are not…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…

Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The…

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as…

There is plenty of theoretical and empirical evidence that depth of neural networks is a crucial ingredient for their success. However, network training becomes more difficult with increasing depth and training of very deep networks remains…

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

How perception and reasoning arise from neuronal network activity is poorly understood. This is reflected in the fundamental limitations of connectionist artificial intelligence, typified by deep neural networks trained via gradient-based…

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging…

In recent years, great success has been witnessed in building problem-specific deep networks from unrolling iterative algorithms, for solving inverse problems and beyond. Unrolling is believed to incorporate the model-based prior with the…

An important challenge in machine learning is to predict the initial conditions under which a given neural network will be trainable. We present a method for predicting the trainable regime in parameter space for deep feedforward neural…

We present a simple non-generative approach to deep representation learning that seeks equivariant deep embedding through simple objectives. In contrast to existing equivariant networks, our transformation coding approach does not constrain…

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…