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Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

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…

Binarization is a powerful compression technique for neural networks, significantly reducing FLOPs, but often results in a significant drop in model performance. To address this issue, partial binarization techniques have been developed,…

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…

As a general type of machine learning approach, artificial neural networks have established state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various kinds of neural networks architectures, polynomial neural…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

Neural Architecture Search (NAS) is a powerful tool to automatically design deep neural networks for many tasks, including image classification. Due to the significant computational burden of the search phase, most NAS methods have focused…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

Neural networks (NNs) struggle to efficiently solve certain problems, such as learning parities, even when there are simple learning algorithms for those problems. Can NNs discover learning algorithms on their own? We exhibit a NN…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

This paper studies the expressive power of artificial neural networks with rectified linear units. In order to study them as a model of real-valued computation, we introduce the concept of Max-Affine Arithmetic Programs and show equivalence…

Modern neural network architectures have achieved remarkable accuracies but remain highly dependent on their training data, often lacking interpretability in their learned mappings. While effective on large datasets, they tend to overfit on…

We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…

The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the…