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We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
We develop a uniform theoretical approach towards the analysis of various neural network connectivity architectures by introducing the notion of a quiver neural network. Inspired by quiver representation theory in mathematics, this approach…
First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
Most existing expressivity theories for neural networks assume exact real arithmetic, whereas practical neural networks are executed under finite-precision floating-point arithmetic with implementation-dependent execution semantics. Recent…
We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience reduced accuracy when working with anatomies that contain numerous junctions or pathological conditions.…
To ensure the correctness of network analysis methods, the network (as the input) has to be a sufficiently accurate representation of the underlying data. However, when representing sequential data from complex systems such as global…
We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…
Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have…
In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machine learning downstream tasks. Our focus is on evaluating…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…
We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural network integrands, computing solutions of a Poisson equation…
Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…
Machine learning is applied to derive microscopically parameters of the interacting boson model for nuclear spectroscopy. A physics-guided neural network is proposed, which is trained to map the potential energy landscapes that are…
Convolutional Neural Networks (CNNs) have been successfully applied to many computer vision tasks, such as image classification. By performing linear combinations and element-wise nonlinear operations, these networks can be thought of as…
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 -…