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Hyperbolic neural networks (HNNs) have demonstrated notable efficacy in representing real-world data with hierarchical structures via exploiting the geometric properties of hyperbolic spaces characterized by negative curvatures. Curvature…

Binary neural networks (BNNs) are an attractive solution for developing and deploying deep neural network (DNN)-based applications in resource constrained devices. Despite their success, BNNs still suffer from a fixed and limited…

DNNs have been quickly and broadly exploited to improve the data analysis quality in many complex science and engineering applications. Today's DNNs are becoming deeper and wider because of increasing demand on the analysis quality and more…

Pre-propagation graph neural networks (PPGNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution -- also theoretically not understood -- concerns their ability to serve as generative models for complicated types of data such as images…

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Bayesian Neural Networks (BNNs) extend traditional neural networks to provide uncertainties associated with their outputs. On the forward pass through a BNN, predictions (and their uncertainties) are made either by Monte Carlo sampling…

Graph neural networks (GNNs) have recently been demonstrated to perform well on a variety of network-based tasks such as decentralized control and resource allocation, and provide computationally efficient methods for these tasks which have…

Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art method for graph-based learning tasks. However, training GCNs at scale is still challenging, hindering both the exploration of more sophisticated GCN architectures and…

We propose Trusted Neural Network (TNN) models, which are deep neural network models that satisfy safety constraints critical to the application domain. We investigate different mechanisms for incorporating rule-based knowledge in the form…

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…

Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike…

A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating…

Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper,…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…