Based on the approach of flow distances, the international trade flow system is studied from the perspective of multi-layer flow network. A model of multi-layer flow network is proposed for modelling and analyzing multiple types of flows in flow systems. Then, flow distances are introduced, and symmetric minimum flow d…
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48 results for “network flows”
Recent work has shown that optical flow estimation can be formulated as a supervised learning task and can be successfully solved with convolutional networks. Training of the so-called FlowNet was enabled by a large synthetically generated dataset. The present paper extends the concept of optical flow estimation via co…
With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be re…
Finite singular times for symmetric network curvature flow.
problem Formation of singularities in network curvature flow.
method Curvature flow of networks with symmetric initial data and two triple junctions.
result The set of singular times is finite.
Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutionsmath.AP
Study hexagonal network evolution under curvature flow.
problem Understanding hexagonal network evolution under curvature flow.
method Proved local existence of classical solutions and classified homothetically shrinking solutions.
result Provided an example of network shrinking to a segment with multiplicity two.
The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale flow monitoring of computer networks under resource constraints. We propose a stochastic optimization framework wh…
Study XRP network, propose Flow Index to analyze transaction frequencies.
problem Analyze transaction frequencies in XRP network.
method Analyze XRP transaction history, propose Flow Index.
result Flow Index reveals bow-tie/walnut structure in XRP network.
Flow-based data sets are necessary for evaluating network-based intrusion detection systems (NIDS). In this work, we propose a novel methodology for generating realistic flow-based network traffic. Our approach is based on Generative Adversarial Networks (GANs) which achieve good results for image generation. A major c…
Coupled Flow Matchingstat.ML
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
Theory explains why neural nets better learn Calabi-Yau metrics.
problem Learning Calabi-Yau metrics with neural networks.
method Developed a theory of metric flows in neural network space.
result Finite-width neural networks learn Calabi-Yau metrics better than fixed kernel methods.
A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all non-source and non-sink nodes. We propose a novel polynomial time algorithm to …
Mirror flow in shallow neural networks shows similar implicit bias to gradient flow, with key differences in curvature penalties.
problem Analyzing implicit bias in shallow neural networks with mirror flow.
method Characterization through variational problems and scaled potentials.
result Mirror flow with scaled potentials induces a rich class of biases not captured by RKHS norms.
Many applications generate data with an intrinsic network structure such as time series data, image data or social network data. The network Lasso (nLasso) has been proposed recently as a method for joint clustering and optimization of machine learning models for networked data. The nLasso extends the Lasso from sparse…
Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
Flow-SSN improves segmentation efficiency and accuracy.
problem Challenges in medical imaging segmentation, especially high-rank pixel-wise covariances.
method Generative segmentation model using discrete-time autoregressive and continuous-time flow variants.
result Flow-SSNs can estimate high-rank pixel-wise covariances efficiently without assuming rank or storing parameters.
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White's local regularity theorem for mean curvature …
Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-det…
Graph neural network using Beltrami flow for feature and topology evolution.
problem Efficient feature learning and topology evolution on graphs.
method Discretized Beltrami flow applied to graph neural networks with positional encodings.
result Achieves state-of-the-art results on various benchmarks.
Study on network flow singularities, focusing on Type-0 singularities.
problem Understanding singularities in network flow evolution.
method Analysis of curvature evolution and junction behavior.
result Bounded curvature for Type-0 singularities in network flow.
Circular Directional Flow Decomposition of Networksphysics.soc-ph
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Normalizing flows are shown to be equivalent to Bayesian networks, revealing new insights.
problem Understanding the limitations and capabilities of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models and analyzing their structure.
result Normalizing flows can be reduced to Bayesian networks, revealing new insights into their structure and capabilities.
The article analyzes the stability of a curve shortening flow for planar networks.
problem Stability analysis of anisotropic curve shortening flow for planar networks.
method Used Lojasiewicz-Simon gradient inequality to derive stability results.
result For initial data close to an energy minimizer, the flow exists globally and converges to a different energy minimum.
Unified survey of elastic flow for curves and networks.
problem Understanding the evolution of curves and networks under elastic forces.
method Unified presentation and proof of global existence and convergence for closed curves.
result Global existence and smooth convergence to critical points for closed curves in R^2.
This study analyzes information flow networks in Chinese stock sectors using transfer entropy.
problem Understanding information transmission and market dynamics in Chinese stock sectors.
method Daily closing price data of 28 sectors from 2000 to 2017, transfer entropy, maximum spanning arborescence (MSA).
result The composite sector is an information source, and the non-bank financial sector is an information sink.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
Study on stability of network flow shrinkers with findings on instability of specific shapes.
problem Stability of regular shrinkers in network flow.
method Analysis of self-similarly shrinking solutions called regular shrinkers.
result All regular shrinkers with two or more enclosed regions can be perturbed away. Specific shapes like 4-ray star, 5-ray star, fish, and rocket are unstable among those with one enclosed region.
Graph neural networks are explained through energy gradient flow and framelet decomposition.
problem Understanding and improving graph neural networks.
method Viewing framelet-based models as gradient flows of energy, proposing a generalized energy via framelet decomposition.
result The proposed model leads to more flexible dynamics, enhancing graph neural networks.
Neural networks predict traffic flow in smart cities.
problem Forecasting stochastic and nonlinear traffic flow.
method Various recurrent neural networks trained on intersection data.
result Vector output model with gated recurrent units performed best.
In this paper, we present a new approach to interpret deep learning models. By coupling mutual information with network science, we explore how information flows through feedforward networks. We show that efficiently approximating mutual information allows us to create an information measure that quantifies how much in…
Study on stochastic mean curvature flow on networks using Ito calculus.
problem Understanding the dynamics of network structures under random influences.
method Application of Ito calculus to derive a stochastic differential equation (SDE) for network edges.
result New insights into the stability, long-term behavior, and pattern formation of complex networks under stochastic influences.
The paper analyzes neural network dynamics after weights escape the origin.
problem Understanding gradient flow dynamics of neural networks after the origin.
method Analyzes gradient flow of homogeneous neural networks with locally Lipschitz gradients.
result Characterizes the first saddle point encountered after escaping the origin.
Study suggests using information flow measures to target interventions in neural networks.
problem Identifying neural network edges that can be pruned to reduce bias.
method Used -information flow framework to measure and compare information flows about true labels and protected attributes, and evaluated pruning effects on bias reduction.
result Pruning edges with larger information flows about protected attributes reduces bias at the output.
Generative flow networks use RL to learn probabilistic models efficiently.
problem Training generative models with RL for compositional discrete objects.
method Reformulate GFlowNet training as entropy-regularized RL with specific reward and regularizer.
result Entropy-regularized RL can be competitive with established GFlowNet training methods.
GC-Flow uses graph flows for better clustering than traditional GCNs.
problem Traditional GCNs miss useful clustering information.
method Designing normalizing flows to replace GCN layers, creating a generative model.
result GC-Flow produces well-separated clusters while maintaining predictive power.
Efficiently quantifies uncertainty in subsurface flow using neural networks guided by theory.
problem Uncertainty in dynamic subsurface flow predictions.
method Theory-guided Neural Network (TgNN) for efficient uncertainty quantification.
result TgNN surrogate improves efficiency of uncertainty quantification compared to MC method.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
Anisotropic curvature flow studied for planar networks.
problem Geometric evolution of planar networks under anisotropic curvature.
method Local existence of classical solutions in the presence of multiple smooth anisotropies.
result Discussion of polycrystalline case aspects.
New method trains any neural network as a generative model.
problem Constrained design of normalizing flows due to analytical invertibility.
method Efficient gradient estimator for non-analytically invertible networks.
result Any dimension-preserving neural network can be used as a generative model.
Gradient flow in ReLU networks biases towards generalization but makes them vulnerable to adversarial attacks.
problem Generalization vs. Adversarial Robustness in ReLU Networks
method Analysis of gradient flow in two-layer ReLU networks with clustered data.
result Gradient flow biases towards generalization but also makes networks vulnerable to adversarial attacks.
Generative Flow Networks solve shortest path problems in graphs.
problem Finding shortest paths in graphs.
method Generative Flow Networks with flow regularization.
result Training a GFlowNet can solve pathfinding problems in arbitrary graphs.
New tensor formulation reveals gradient flow's bias in linear neural networks.
problem Understanding implicit bias in linear neural network training.
method Tensor formulation of neural networks, including fully-connected, diagonal, and convolutional networks.
result Gradient flow on linear tensor networks converges to solutions of specific optimization problems.
This study explains gradient flow dynamics in neural networks for small initialisation.
problem Understanding the training dynamics of neural networks for small initialisation.
method Analysis of gradient flow dynamics for one-hidden layer ReLU networks with orthogonal inputs.
result Gradient flow converges to zero loss and characterizes implicit bias towards minimum variation norm.
DIGRAC clusters directed graphs using flow imbalance, outperforming existing methods.
problem Clustering directed networks without label supervision.
method DIGRAC uses a graph neural network with a novel imbalance loss for directed flow imbalance.
result DIGRAC outperforms 10 state-of-the-art methods on directed graph clustering.
Study examines money flow network among firms' accounts in a Japanese region.
problem Understanding the relationship between money flow and economic activities of firms.
method Employed exhaustive bank transfer data, network statistics, Hodge decomposition, and non-negative matrix factorization.
result Identified a 'walnut' structure with core and upstream/downstream components, correlated with economic activities.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the…
Flowification enriches neural networks with an inverse pass and likelihood monitoring.
problem Neural networks lack an inverse pass and likelihood monitoring, limiting their generative capabilities.
method Introduce flowification, enriching neural networks with a stochastic inverse pass and likelihood monitoring.
result Certain neural network architectures can be enriched to fall under the generalized notion of a normalizing flow.
The paper analyzes how GANs converge using dual metric flows.
problem Understanding the convergence dynamics of GANs.
method Investigates the convergence of GANs using dual metric flows, formal definitions, and proving convergence.
result GAN learning dynamics converge to a limit when learning rate is small.