Related papers: Higher-order interaction model from geometric meas…

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…

In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…

In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing…

We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

When networked systems of autonomous agents carry out complex tasks, the control and coordination sought after generally depend on a few fundamental control primitives. Chief among these primitives is consensus, where agents are to converge…

A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic…

We propose OneFlow - a flow-based one-class classifier for anomaly (outlier) detection that finds a minimal volume bounding region. Contrary to density-based methods, OneFlow is constructed in such a way that its result typically does not…

We define a higher order Deffuant model by generalizing the original pairwise interaction model for bounded-confidence opinion-dynamics to interactions involving a group of agents of size k. The generalized model is naturally encoded in a…

The approach to decomposition of multidimensional network systems on monoflow multilayer network systems (MLNS) is proposed, which significantly simplifies the analysis of intersystem interactions in multipurpose and multifunctional…

In this paper, we present a new self-supervised scene flow estimation approach for a pair of consecutive point clouds. The key idea of our approach is to represent discrete point clouds as continuous probability density functions using…

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…

A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…

Finding image correspondences remains a challenging problem in the presence of intra-class variations and large changes in scene layout.~Semantic flow methods are designed to handle images depicting different instances of the same object or…

This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…

In this paper, we propose a convolutional layer inspired by optical flow algorithms to learn motion representations. Our representation flow layer is a fully-differentiable layer designed to capture the `flow' of any representation channel…

The paper proposes a surprisingly simple characterization of a large class of models of distributed computing, via an agreement function: for each set of processes, the function determines the best level of set consensus these processes can…

Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…

We present a generalized Lohe matrix model for a homogeneous ensemble with higher order couplings via the gradient flow approach. For the homogeneous free flow with the same hamiltonian, it is well known that the Lohe matrix model with…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…