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Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline…

In the semantic segmentation of remote sensing images, acquiring complete ground objects is critical for achieving precise analysis. However, this task is severely hindered by two major challenges: high intra-class variance and high…

We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically what deep learning practitioners have long observed…

Deep learning-based applications have seen a lot of success in recent years. Text, audio, image, and video have all been explored with great success using deep learning approaches. The use of convolutional neural networks (CNN) in computer…

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…

There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Deep learning techniques have been successfully applied in many areas of computer vision, including low-level image restoration problems. For image super-resolution, several models based on deep neural networks have been recently proposed…

In this paper, we describe the deep sparse coding network (SCN), a novel deep network that encodes intermediate representations with nonnegative sparse coding. The SCN is built upon a number of cascading bottleneck modules, where each…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

A number of studies have shown that increasing the depth or width of convolutional networks is a rewarding approach to improve the performance of image recognition. In our study, however, we observed difficulties along both directions. On…

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…

While deeper and wider neural networks are actively pushing the performance limits of various computer vision and machine learning tasks, they often require large sets of labeled data for effective training and suffer from extremely high…

End-to-end deep-learning networks recently demonstrated extremely good perfor- mance for stereo matching. However, existing networks are difficult to use for practical applications since (1) they are memory-hungry and unable to process even…

We propose Nester, a method for injecting neural networks into constrained structured predictors. The job of the neural network(s) is to compute an initial, raw prediction that is compatible with the input data but does not necessarily…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

Autonomous vehicles and robots require a full scene understanding of the environment to interact with it. Such a perception typically incorporates pixel-wise knowledge of the depths and semantic labels for each image from a video sensor.…