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In the past two decades we have seen the popularity of neural networks increase in conjunction with their classification accuracy. Parallel to this, we have also witnessed how fragile the very same prediction models are: tiny perturbations…
In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…
Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…
Verifying real-world programs often requires inferring loop invariants with nonlinear constraints. This is especially true in programs that perform many numerical operations, such as control systems for avionics or industrial plants.…
In many real-world problems, collecting a large number of labeled samples is infeasible. Few-shot learning (FSL) is the dominant approach to address this issue, where the objective is to quickly adapt to novel categories in presence of a…
In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…
Satisfiability modulo nonlinear real arithmetic theory (SMT(NRA)) solving is essential to multiple applications, including program verification, program synthesis and software testing. In this context, recently model constructing…
Deep neural networks (DNNs) have achieved the state of the art performance in numerous fields. However, DNNs need high computation times, and people always expect better performance in a lower computation. Therefore, we study the human…
Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…
Deep Learning Accelerators are prone to faults which manifest in the form of errors in Neural Networks. Fault Tolerance in Neural Networks is crucial in real-time safety critical applications requiring computation for long durations. Neural…
Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…
We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this viewpoint, we establish detailed connections between the…
Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…
Graph neural networks (GNNs) have demonstrated superior performance in collaborative recommendation through their ability to conduct high-order representation smoothing, effectively capturing structural information within users' interaction…
Deep neural networks (DNNs) excel in computer vision tasks, especially, few-shot learning (FSL), which is increasingly important for generalizing from limited examples. However, DNNs are computationally expensive with scalability issues in…