Related papers: Emergent Higher-Order Structure from Fast Adaptive…

We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…

Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…

The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could collapses to a two-dimensional system of order differential equations with it. In this paper, we propose the ensemble order parameter (EOP)…

Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…

We study a system of $N$ interacting particles moving on the unit sphere in $d$-dimensional space. The particles are self-propelled and coupled all to all, and their motion is heavily overdamped. For $d=2$, the system reduces to the classic…

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…

Federated Learning is a popular distributed learning paradigm in machine learning. Meanwhile, composition optimization is an effective hierarchical learning model, which appears in many machine learning applications such as meta learning…

Gradient Boosting Decision Trees (GBDTs) dominate tabular machine learning, with modern implementations like XGBoost, LightGBM, and CatBoost being based on Newton boosting: a second-order descent step in the space of decision trees. Despite…

Message passing is the core operation in graph neural networks, where each node updates its embeddings by aggregating information from its neighbors. However, in deep architectures, this process often leads to diminished expressiveness. A…

We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid…

One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

The number $\mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining…

Transformers have emerged as the state of the art neural network architecture for natural language processing and computer vision. In the foundation model paradigm, large transformer models (BERT, GPT3/4, Bloom, ViT) are pre-trained on…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…