Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.
problem Improving graph self-supervised learning performance without labeled data.
method Graph Interplay (GIP) introduces random inter-graph edges within standard batches to enhance GSSL methods.
result GIP significantly outperforms existing GSSL methods across multiple benchmarks.
Learning to cooperate is crucially important in multi-agent environments. The key is to understand the mutual interplay between agents. However, multi-agent environments are highly dynamic, where agents keep moving and their neighbors change quickly. This makes it hard to learn abstract representations of mutual interp…
Graph Laplacians and machine learning predict properties of finite graphs.
problem Understanding properties of finite graphs using spectral and topological methods.
method Combining graph Laplacians, spectral inequalities, machine learning, and topological data analysis.
result Neural networks can accurately predict graph properties like Ricci-flatness and spectral gaps.
New method separates graph structure from node attributes to recover lost signal.
problem Standard representation learning on attributed graphs merges incompatible metric spaces, leading to geometrically flawed alignment.
method Custom variational autoencoder that separates manifold learning from structural alignment.
result Transforms geometric conflict into interpretable structural descriptor, uncovering connectivity patterns and anomalies.
The paper calculates genus bounds for multibranched surfaces.
problem Finding genus bounds for multibranched surfaces.
method Using the first Betti number and boundary genus, the paper provides lower bounds for maximum and minimum genus.
result The maximum and minimum genus of GimesS1 equals twice that of G. Study how communication and feedback graphs affect learning outcomes.
problem Understanding the impact of feedback graphs on cooperative online learning.
method Analyzed network regret in terms of the independence number of the strong product of communication and feedback graphs.
result Proved bounds for network regret and demonstrated the non-improvable nature of positive results in pathological cases.
Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.
problem Insufficient theoretical understanding of GNNs' generalization behavior.
method Develop a balanced theory focusing on expressive power, generalization, and optimization.
result Theoretical advancements need to align with practical success in graph machine learning.
Generative model controls heterophily in graph signals.
problem Controlling heterophily in graph signals for better model effectiveness.
method Combines graphon-based generator with spectral filtering of Gaussian node features.
result Establishes theoretical guarantees for heterophily control and convergence.
In contrast with knots, whose properties depend only on their extrinsic topology in S3, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S3 . For example, it was shown in [2] that every embedding of the complete graph K7 in S3 …
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture call…
New algorithm improves bandit with graph feedback by decomposing regret.
problem Improving performance in bandit problems with graph feedback.
method Partition-based algorithm framework using regret decomposition.
result Improved and optimal regret bounds on various graph families.
Paper proposes AI for stock market forecasting using external knowledge.
problem Forecasting stock prices influenced by external factors.
method Learning from historical data and external temporal knowledge graphs modeled as Hawkes processes.
result Dynamic representations effectively rank stocks based on returns.
Study on stability of GCNNs under graph perturbations.
problem Limited theoretical understanding of GCNN stability.
method Proposes a probabilistic framework to analyze GCNN stability under various graph perturbations.
result Demonstrates the importance of data distribution in stability analysis.
Hypercube graphs are optimal in spectral rigidity due to Bakry--Émery curvature.
problem Spectral rigidity of hypercube graphs
method Interplay between global spectral embedding and local curvature analysis
result Hypercube graphs are optimal in spectral rigidity due to Bakry--Émery curvature.
GNNs generalize better on homophilic graphs than heterophilic ones.
problem Understanding the generalization error of GNNs on graph data.
method Analytical tools from statistical physics and random matrix theory.
result Risk is shaped by graph noise, feature noise, and training labels.
DGRCL integrates dynamic and static graph relations for financial market prediction.
problem Capturing the evolving nature of stock markets while considering both temporal changes and static relational structures.
method Dynamic Graph Representation with Contrastive Learning (DGRCL) framework, including Embedding Enhancement (EE) and Contrastive Constrained Training (CCT) modules.
result DGRCL significantly outperforms state-of-the-art TGL baselines on NASDAQ and NYSE datasets.
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However…
The paper proposes Tier Balancing for dynamic fairness in decision-making.
problem Achieving long-term fairness in decision-making processes.
method Causal modeling with DAGs to investigate dynamic fairness.
result Tier Balancing is a more natural approach to achieve long-term fairness, capturing latent causal factors.
Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI…
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block m…
GNNs improve brain activity forecasting in fMRI studies.
problem Understanding neural dynamics in the brain.
method Comparison of GNN architectures for modeling fMRI data.
result GNNs outperform VAR models in robustly scaling to large network studies.
This work analyzes Fréchet regression using comparison geometry, providing theoretical and practical insights.
problem Analyzing data on complex structures like manifolds and graphs.
method Theoretical analysis through comparison geometry, focusing on existence, uniqueness, and stability of the Fréchet mean.
result Key results on the existence, uniqueness, and stability of the Fréchet mean, along with statistical guarantees for nonparametric regression.
SSL theory improves representation learning from raw data.
problem Challenges in SSL, including instability and collapse.
method Precise analysis of generalization performance with a theory-friendly setup.
result Insights for SSL practitioners on data augmentation, network architecture, and training algorithm.
Enhances community detection in correlated networks with node attributes.
problem Community detection in multiple networks with correlated node attributes and edges.
method Introduced the correlated Contextual Stochastic Block Model (CSBM), developed a two-step matching procedure.
result Algorithm recovers exact node correspondence, enabling enhanced community detection.
Deep learning models simulate complex karst network patterns.
problem Complex karst network patterns due to hydrogeological conditions.
method Graph generative models (GraphRNN and G-DDPM) to capture topological and spatial properties.
result Stochastic simulation of karst networks across various formations.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced k-local and k-global functions to study the interplay between depth and function locality. result Depth is beneficial for learning local functions but detrimental to learning global functions.
The paper extends manifold learning to arbitrary norms, improving molecular motion mapping.
problem Improving manifold learning for non-Euclidean norms.
method Determines the limiting differential operator for graph Laplacians using any norm.
result A modified Laplacian eigenmaps algorithm using Earthmover's distance outperforms Euclidean methods in molecular motion mapping.
The paper explores holonomy, zeta functions, and cohomology in foliated manifolds with stratified boundaries.
problem Understanding symmetries and cohomology in foliated manifolds with stratified boundaries.
method Developed a novel formalism for the Gamma-set and defined an Ihara zeta function to encode symmetries. Investigated the relationship between holonomy and zeta functions, and analyzed how the twist map impacts cohomology.
result Conjectured a duality between holonomy fixed points and the poles of the Ihara zeta function, extending to twisted cohomology classes.
Criteria for embedding simplicial complexes into manifolds, reducing a topological problem to algebra.
problem Embedding simplicial complexes into manifolds.
method Interplay between geometric topology, combinatorics, and linear algebra; calculation of generators in configuration space homology.
result Criteria for Z2-embeddability of certain simplicial complexes to 2k-dimensional manifolds. Algorithm learns graph operator from sparse space-time samples.
problem Learning time-varying graph signals from partial observations.
method Non-convex IRLS algorithm for low-rank matrix completion.
result No more than O(rn log(nT)) space-time samples needed for accurate recovery.
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary mechanism responsible for the observed long-range dependence and statistical propertie…
MAPPING debiases GNNs for fair node classification with limited leakage.
problem Graph Neural Networks inherit and exacerbate historical discrimination in high-stake domains.
method MAPPING uses distance covariance-based fairness constraints and adversarial debiasing.
result MAPPING achieves better trade-offs between fairness and utility, mitigating privacy risks.
Algorithm finds Dirichlet domains for hyperbolic surfaces.
problem Computing explicit Dirichlet domains for hyperbolic surfaces.
method Algorithm based on side pairings of fundamental polygons, using geometric-topological data structures.
result Algorithm runs in polynomial time, dependent on surface perimeter and genus.
The production and consumption of information about Bitcoin and other digital-, or 'crypto'-, currencies have grown together with their market capitalisation. However, a systematic investigation of the relationship between online attention and market dynamics, across multiple digital currencies, is still lacking. Here,…
The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.
Quantum crypto-economics models price risks in blockchain technology.
problem Quantum technology's potential to undermine blockchain security.
method Building financial models to price quantum risk in blockchain scenarios.
result Quantum crypto-economics models can assess and price quantum risks in blockchain.
Users increasingly rely on social media feeds for consuming daily information. The items in a feed, such as news, questions, songs, etc., usually result from the complex interplay of a user's social contacts, her interests and her actions on the platform. The relationship of the user's own behavior and the received fee…
Researchers found a quadratic estimate for embedding higher-dimensional simplices into sphere-connected sums.
problem Estimating the number of handles required for embedding higher-dimensional simplices into sphere-connected sums.
method Combining geometric topology, combinatorics, and linear algebra.
result Presented a quadratic estimate g≥ckn2 for embedding k-faces of n-simplex. This work explores how overparametrization and priors affect Bayesian neural network posteriors.
problem Symmetries, non-identifiabilities, and weight-space priors fragment and inflate BNN posteriors.
method We study the interplay between overparametrization and priors in BNN posteriors, deriving key phenomena and validating through experiments.
result Overparametrization induces structured, prior-aligned weight posterior distributions.
Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameterized convolutional net…
The paper extends group constructions to coset geometries, creating new ways to combine geometries.
problem Combining and gluing incidence geometries in a general framework.
method Extending classical group-theoretic constructions to coset geometries.
result Provides a general framework for combining or gluing incidence geometries.
This is an introduction to the algebraic aspect of Teichmüller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.
Study on properties of special Kähler metrics and their interplay.
problem Properties and interplay of Strong Kähler with torsion and astheno-Kähler metrics.
method Analyzes families of astheno-Kähler nilmanifolds, studies complex blowups, and investigates interplay between metrics.
result Existence of astheno-Kähler metrics is not preserved by blowup, and some metrics are geometrically Bott-Chern formal.
We investigate a family of regression problems in a semi-supervised setting. The task is to assign real-valued labels to a set of n sample points, provided a small training subset of N labeled points. A goal of semi-supervised learning is to take advantage of the (geometric) structure provided by the large number o…
We survey some topics in A1-homotopy theory. Our main goal is to highlight the interplay between A1-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various standpoints.
We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topological characterization of those compact 3-manifolds that support Riemannian metrics of positive scalar curvature and mean-convex boundary and…
New construction of Turaev-Viro invariants invariant under Morita equivalence.
problem Constructing Turaev-Viro invariants invariant under Morita equivalence.
method Pivotal bicategory construction of spherical module categories.
result The invariant recovers the standard Turaev-Viro invariant and is independent of the skeleton.
Develops MgCSL for discovering causal structures in high-dimensional data.
problem Discovering causal relationships from high-dimensional data with complex interplay of variables.
method MgCSL uses sparse auto-encoders for coarse-graining and multi-layer perceptrons for detailed analysis, introducing simplified acyclicity constraints.
result MgCSL outperforms existing methods and finds explainable causal connections in fMRI datasets.