Related papers: Make flows small again: revisiting the flow framew…
Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…
Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
Developing of an effective flow control algorithm to avoid congestion is a hot topic in computer network society. This document gives a mathematical model for general network at the beginning, and then discrete control theory is proposed as…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
Unsupervised optical flow estimators based on deep learning have attracted increasing attention due to the cost and difficulty of annotating for ground truth. Although performance measured by average End-Point Error (EPE) has improved over…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their…
Optical flow estimation can be formulated as an end-to-end supervised learning problem, which yields estimates with a superior accuracy-runtime tradeoff compared to alternative methodology. In this paper, we make such networks estimate…
Uncovering rationales behind predictions of graph neural networks (GNNs) has received increasing attention over the years. Existing literature mainly focus on selecting a subgraph, through combinatorial optimization, to provide faithful…
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
Part II of this paper elaborates on the unique capability of the proposed power flow analysis framework to obtain the true solution corresponding to the stable operating point of a network. It explains the significance of obtaining the true…
We develop a theoretical framework for defining and identifying flows of information in computational systems. Here, a computational system is assumed to be a directed graph, with "clocked" nodes that send transmissions to each other along…
When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be…