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Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since…

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…

Recent efforts in applying implicit networks to solve inverse problems in imaging have achieved competitive or even superior results when compared to feedforward networks. These implicit networks only require constant memory during…

Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but…

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…

A common practice in most of deep convolutional neural architectures is to employ fully-connected layers followed by Softmax activation to minimize cross-entropy loss for the sake of classification. Recent studies show that substitution or…

The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…

A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in…

Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in…

Training a deep neural network with the outputs of selected layers satisfying linear constraints is required in many contemporary data-driven applications. While this can be achieved by incorporating projection layers into the neural…

Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation, the workhorse for…

Jacobian-vector products (JVPs) form the backbone of many recent developments in Deep Networks (DNs), with applications including faster constrained optimization, regularization with generalization guarantees, and adversarial example…

Deep Neural Networks are successful but highly computationally expensive learning systems. One of the main sources of time and energy drains is the well known backpropagation (backprop) algorithm, which roughly accounts for 2/3 of the…

In recent years deep neural networks have been successfully applied to the domains of reinforcement learning \cite{bengio2009learning,krizhevsky2012imagenet,hinton2006reducing}. Deep reinforcement learning \cite{mnih2015human} is reported…

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…

Recent advances in deep neural networks (DNNs) owe their success to training algorithms that use backpropagation and gradient-descent. Backpropagation, while highly effective on von Neumann architectures, becomes inefficient when scaling to…

Deep equilibrium models (DEQs) have proven to be very powerful for learning data representations. The idea is to replace traditional (explicit) feedforward neural networks with an implicit fixed-point equation, which allows to decouple the…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

The training of deep neural nets is expensive. We present a predictor- corrector method for the training of deep neural nets. It alternates a predictor pass with a corrector pass using stochastic gradient descent with backpropagation such…

Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes…