Graph Cascades rewire graphs to improve structure-aware learning.
problem Improving graph neural networks and transformers for structure-aware learning.
method Graph Cascades uses contagion-based diffusion processes to construct an auxiliary graph with reinforced edges.
result Graph Cascades improves node-classification benchmarks across various graph types.
FoSR adds edges to graphs to prevent oversquashing and oversmoothing in GNNs.
problem Oversquashing and oversmoothing in graph neural networks (GNNs).
method First-order spectral rewiring to add edges based on spectral expansion, combined with a relational architecture.
result Our algorithm outperforms existing graph rewiring methods in graph classification tasks.
Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which deliberately add carefully created unnoticeable perturbation to the graph structure. …
Graph rewiring method alleviates over-squashing in GNNs.
problem Over-squashing and bottlenecks in graph neural networks.
method Curvature-based graph rewiring method.
result Negatively curved edges cause over-squashing in GNNs.
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
TGR rewires temporal graphs to improve TGNN performance.
problem Temporal graphs in evolving networks can suffer from under-reaching and over-squashing issues.
method TGR uses expander graph propagation to create message-passing highways between temporally distant nodes.
result TGR achieves state-of-the-art results on temporal graph benchmarks.
New method uses curvature to improve graph neural networks.
problem Graph Neural Networks struggle with over-smoothing and over-squashing.
method Augmented Forman-Ricci curvature (AFRC) for scalable rewiring.
result AFRC effectively mitigates over-smoothing and over-squashing.
Rewiring GNNs to optimize community and feature alignment improves their performance.
problem Improving GNNs' performance by addressing over-squashing and generalization issues.
method Three rewiring strategies: ComMa, FeaSt, and ComFy, targeting community structure, node labels, and their alignment.
result Rewiring strategies enhance GNNs' performance by optimizing label-community alignment.
Paper proposes JDR to denoise graph features and rewire graphs for better node classification.
problem Jointly denoise noisy graph features and rewire graphs for improved node classification.
method Align leading spectral spaces of graph and feature matrices to solve non-convex optimization problem.
result JDR consistently outperforms existing methods on various node classification tasks.
Rewiring networks using discrete geometry improves GNN training accuracy and reduces runtime.
problem Inefficient information propagation between distant nodes in graph neural networks.
method Discrete analogues of classical geometric curvature to model and rewire networks.
result Classical geometric notions achieve state-of-the-art GNN training accuracy and significantly reduce runtime.
This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural n…
DRew dynamically rewires message passing to improve long-range tasks.
problem Over-squashing in MPNNs due to local message passing.
method Layer-dependent rewiring and delay mechanism for gradual densification.
result DRew outperforms graph Transformers and multi-hop MPNNs on long-range tasks.
Paper proposes LCP for structural encodings, outperforming existing methods.
problem Improving Graph Neural Networks performance through effective structural encodings.
method Geometric perspective, Local Curvature Profiles (LCP) for structural encodings, combining with global positional encodings, comparing with rewiring techniques.
result LCP significantly outperforms existing structural encodings and combining LCP with global positional encodings improves performance.
Neuromorphic hardware tends to pose limits on the connectivity of deep networks that one can run on them. But also generic hardware and software implementations of deep learning run more efficiently for sparse networks. Several methods exist for pruning connections of a neural network after it was trained without conne…
CT improves neural network performance on cell complex data.
problem Improving predictive performance of neural networks on complex data.
method Introducing the Cellular Transformer (CT) that generalizes graph-based transformers to cell complexes.
result CT achieves state-of-the-art performance on cell complex datasets without complex enhancements.
ECGs improve GNNs for non-homophilic data.
problem Improving GNNs for datasets where nodes are not likely to belong to the same class.
method ECGs rewire GNNs' computation graph to connect nodes likely in the same class using weaker classifiers.
result ECGs improve GNN performance on non-homophilic datasets.
This paper improves GNN efficiency for large-scale graph applications.
problem High memory usage and computational costs in large-scale graph applications.
method Sparsification techniques from Network Science and Machine Learning.
result Adaptive rewiring enhances GNN performance and scalability.
Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of {\it Drosophila melanogaster} can exhibit significant topological changes to facilitate dynamic regulatory functions. Thus it is essential to develop methodologies that capture the temporal evolut…
Graphs can be smoothed or squashed too, study finds.
problem Graph Neural Networks struggle with over-smoothing and over-squashing issues.
method Unified framework using Ollivier-Ricci curvature to address both issues.
result Over-smoothing and over-squashing linked to positive and negative graph curvature respectively.
This paper examines properties of feedforward graphs to improve neural network performance.
problem The choice of computational graph can significantly impact neural network performance.
method The paper introduces two measures: fidelity and mixing time, and evaluates popular graphs using these measures.
result Popular graphs are evaluated based on fidelity and mixing time, revealing their performance implications.
Cellina uses supervised disentanglement to predict cell behavior in tissues.
problem Querying counterfactuals on tissue graphs
method Cellina framework using supervised disentanglement
result Outperforms spatially-informed and non-spatial competitors
MPNNs over-squash distant node information, study shows.
problem Over-squashing in MPNNs where node features ignore distant nodes.
method Theoretical analysis of MPNNs' over-squashing, focusing on width, depth, and graph topology.
result Width mitigates over-squashing but makes network more sensitive, depth doesn't help, graph topology is key.
Framework for analyzing dynamic topological changes in point clouds using persistent homology and dynamic optimal transport.
problem Analyzing transient structural reorganizations during dynamic phase transitions in time-evolutionary point clouds.
method Hierarchical dynamic evaluation framework driven by topological and hypergraph reconstruction strategy.
result Combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.
We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including maximum likelihood estimation algorithms. We discuss models of this type and their pro…
We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theore…
MPNNs struggle with class-bottlenecks and heterophily, leading to performance limitations.
problem Performance limitations of MPNNs under heterophily and structural bottlenecks.
method A statistical framework decomposing model performance into SNR components and proving bounds on sensitivity.
result Optimal graph structures for maximizing higher-order homophily are disjoint unions of single-class and two-class-bipartite clusters.
We analyze cascades of defaults in an interbank loan market. The novel feature of this study is that the network structure and the size distribution of banks are derived from empirical data. We find that the ability of a defaulted institution to start a cascade depends on an interplay of shock size and connectivity. Fu…
We study insolvency cascades in an interbank system when banks are allowed to insure their loans with credit default swaps (CDS) sold by other banks. We show that, by properly shifting financial exposures from one institution to another, a CDS market can be designed to rewire the network of interbank exposures in a way…
Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varyin…
New Riemannian GNNs reduce over-squashing in graphs with negative curvature.
problem Over-squashing in Riemannian graph neural networks.
method Generalization of Hyperbolic GNNs to Riemannian manifolds of variable curvature.
result Bounds on sensitivity of node features in Riemannian GNNs as layers increase.
Paper detects anomalous edges in social networks using edge exchangeability.
problem Detecting anomalous edges in directed social networks.
method Exploits edge exchangeability and uses conformal prediction theory.
result Proposed anomaly detector has a guaranteed upper bound for false positives.
Study uses Google matrix analysis to show how COVID-19 changed international trade flows.
problem Impact of COVID-19 on international trade patterns.
method Google matrix analysis of World Trade Network (WTN), including PageRank, CheiRank, and reduced Google matrix.
result Significant changes in international trade flows due to the pandemic, affecting export and import balances.
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify relations between singularities of parallel and dual surfaces and differential geometri…
OL4EL optimizes edge learning on resource-constrained servers.
problem Resource constraints on edge servers hinder effective distributed machine learning.
method Online Learning for EL (OL4EL) framework using budget-limited multi-armed bandit model.
result OL4EL significantly improves learning performance while conserving resources.
New GPs model edge functions on complex networks, capturing divergence and curl.
problem Modeling flow data on networks with independent learning of Hodge components.
method Developed Hodge-compositional edge GPs using Hodge decomposition.
result Hodge-compositional edge GPs can represent any edge function and capture flow relevance.
In L^3, cuspidal edges can have bounded mean curvature under specific conditions.
problem Understanding cuspidal edges with bounded mean curvature in Lorentz-Minkowski 3-space.
method Investigated cuspidal edges and generalized cuspidal edges, analyzing their singular points and principal curvatures.
result Cuspidal edges with bounded mean curvature in L^3 occur only when the singular set is a light-like curve.
Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field ν is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
Edge augmentation connects disconnected graphs by elevating eigenvalues.
problem Connecting disconnected subgraphs in graphs with zero eigenvalues.
method Elevating zero eigenvalues of graph's spectrum to connect subgraphs.
result The algorithm consistently connects graph components, achieving >50% inter-community edges.
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…
In the emerging advancement in the branch of autonomous robotics, the ability of a robot to efficiently localize and construct maps of its surrounding is crucial. This paper deals with utilizing thermal-infrared cameras, as opposed to conventional cameras as the primary sensor to capture images of the robot's surroundi…
Study of cuspidal edges on focal surfaces of regular surfaces.
problem Clarifying the sign of singular curvature at cuspidal edges.
method Investigation using singularities of parallel surfaces.
result Clarification of the sign of singular curvature at cuspidal edges.
The paper introduces a new method to improve model generalization by routing model copies through permutations.
problem Improving model generalization in machine learning.
method The method replicates a model \(M\) times and rewire the contexts in which local learning messages are computed using permutations.
result The method improves generalization by structured message sharing rather than coupling parameters.
Method certifies edge predictions with cloud-level reliability.
problem Ensuring reliability of edge intelligence models.
method Conformal alignment-based cascading mechanism.
result Certifies conditional coverage with user control over risk level.
Defense against user shilling attacks in collaborative filtering using edge reweighting.
problem Vulnerability of collaborative filtering to profile injection attacks.
method Adversarial robustness based edge reweighting to attenuate non-robust edges.
result Effective defense against various types of attacks demonstrated through experiments.
A hybrid neural network optimizes AI deployment on edge and cloud for energy efficiency.
problem Energy and resource constraints in edge devices for deep learning models.
method Conditionally deep hybrid neural network with quantized layers at edge and full-precision layers at cloud.
result Early classification at the edge reduces energy consumption by 5.5x on CIFAR-10 dataset.
CoMGNN models heterogeneous graphs with evolving nodes and edges.
problem Modeling complex, evolving graphs with diverse information.
method Meta graph attention on co-evolving heterogeneous graphs.
result Significant improvement over state-of-the-art methods.