TAGCN improves graph CNN performance without approximation.
problem Performance loss in spectral graph convolutional neural networks.
method Topology adaptive graph convolutional network (TAGCN) with adaptive filters.
result TAGCN outperforms existing spectral CNNs on various datasets.
Enhanced binary classifier uses Urysohn's Lemma of Topology.
problem Binary classification challenges.
method Utilizes Urysohn's Lemma of Topology to construct separating functions.
result Exceptional performance in numerical experiments (95% to 100%).
Study of digital topology concepts like hyperspaces and function graphs.
problem Adapting classical topology concepts to digital topology.
method Define digital hyperspaces and function graphs, study their properties.
result Some relationships and graphical properties of digital hyperspaces and function graphs.
This work introduces a method to compare sparse neural network topologies using graph theory.
problem Comparing and understanding sparse neural network topologies, especially during training.
method Introducing Neural Network Sparse Topology Distance (NNSTD) to measure distances between different sparse neural networks.
result Sparse neural networks can outperform over-parameterized models without further structure optimization.
Algorithm learns graph topologies to adapt labels between source and target graphs.
problem Domain adaptation on graphs with different data manifolds.
method Proposes a graph domain adaptation algorithm that learns both graph topologies and label functions.
result Improves classification performance as graph topologies become more balanced.
An adaptive clustering algorithm learns from evolving data without manual tuning.
problem Clustering in dynamic data environments where distributions change over time.
method ART-based topological clustering with self-adjusting vigilance parameter.
result The algorithm outperforms state-of-the-art methods in clustering performance and continual learning.
Detects financial fraud schemes in networks using graph structure learning.
problem Identifying financial fraud schemes in complex networks.
method Adapting dictionary learning to network topologies, imposing Laplacian structure on dictionaries.
result Proposed methods effectively represent graph structure information for anomaly detection.
EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
Proposes GLNNs for robust semi-supervised classification using adaptive graphs.
problem Adaptive graph learning for robust semi-supervised classification.
method Optimizes graph structure from data and tasks using spectral graph theory and maximum a posteriori estimation.
result GLNNs outperform state-of-the-art approaches in semi-supervised classification.
We give a surface for which the Ricci Flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci Flow perturbation and then we construct a surface which is closely related to a surface of revolution, but does not quite have…
Two short proofs show intersection homology's stability.
problem Topological invariance of intersection homology.
method Two proofs: one short requiring support and cosupport axioms, the other longer adaptable to more perversities.
result Intersection homology's stability proven without axioms.
A novel framework for adaptive multi-agent communication in reinforcement learning.
problem Manual specification of communication structures in multi-agent reinforcement learning.
method Learning Structured Communication (LSC) framework using hierarchical graph neural networks.
result Adaptive hierarchical formations and efficient message propagation among agents.
AdaCGP learns dynamic graph topology from time series data, improving over existing methods.
problem Learning dynamic graph topology from time-varying signals, especially in real-time applications.
method AdaCGP is a sparsity-aware adaptive algorithm that recursively estimates the Graph Shift Operator (GSO) through variable splitting.
result AdaCGP outperforms state-of-the-art methods in GSO estimation, achieving improvements exceeding 83%.
Defines new rho invariant for topological groups.
problem No specific problem stated; focuses on new invariant.
method Adapts Weinberger's work using differential geometry.
result Defines additive higher rho invariant for structure groups.
We introduce Graphical TREX (GTREX), a novel method for graph estimation in high-dimensional Gaussian graphical models. By conducting neighborhood selection with TREX, GTREX avoids tuning parameters and is adaptive to the graph topology. We compare GTREX with standard methods on a new simulation set-up that is designed…
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Unified analysis for decentralized SGD across various topologies and updates.
problem Analysis of decentralized SGD methods with changing topologies and local updates.
method Unified convergence analysis covering local SGD updates and adaptive network topology.
result Universal convergence rates for smooth problems, interpolating between heterogeneous and iid-data settings.
This paper considers the problem of adaptively searching for an unknown target using multiple agents connected through a time-varying network topology. Agents are equipped with sensors capable of fast information processing, and we propose a decentralized collaborative algorithm for controlling their search given noisy…
GCNN research tackles graph data topology and prediction.
problem Graphs' irregularity and complexity make traditional CNN methods unsuitable.
method Review and categorization of GCNN techniques.
result TAGCN approach shows promise for improving graph data prediction.
We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological spaces and prove an analogue of the approximation theorem. Namely…
PEAR dynamically reconfigures agent roles to prevent persistent biases in multi-agent debates.
problem Persistent positional biases and sensitivity to role assignments in fixed topologies.
method Dynamic reconfiguration of agent roles and sparse topologies based on evolving agent states.
result Significantly improves average accuracy over debate baselines across multiple reasoning benchmarks.
Topology-GS improves 3D GS for better structural and feature integrity.
problem Compromised pixel-level and feature-level integrity in 3D GS.
method Incorporates Local Persistent Voronoi Interpolation (LPVI) and PersLoss based on persistent homology.
result Topology-GS outperforms existing methods in PSNR, SSIM, and LPIPS metrics.
Paper speeds up topological signal identification and cycle matching.
problem Efficiently identifying and matching topological signals across datasets.
method Cohomological approach to persistent homology computation.
result Significantly faster performance on large-scale datasets.
Enhanced neural network framework improves constraint satisfaction with topological conditioning.
problem Maintaining semantic coherence while satisfying physical and logical constraints in neuro-symbolic reasoning.
method Integrates topological conditioning with gradient stabilization mechanisms using Forman-Ricci curvature, Deep Delta Learning, and Covariance Matrix Adaptation Evolution Strategy.
result Achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate.
New adaptive tests improve statistical dependence detection.
problem Testing statistical dependence between multivariate variables.
method Adaptive nonlinear monotonic transformations of distances.
result Empirical tests outperform existing methods.
Network agents solve adaptive regression problems with compressed signals.
problem Solving regression problems in networks with communication constraints.
method ACTC diffusion strategy with randomized differential compression.
result Optimized resource allocation improves performance.
Enhances graph embeddings by preserving graph topology.
problem Node2vec struggles to recreate the topology of input graphs.
method Introduces a topological loss term to Node2vec, aligning the persistence diagram of the embedding to that of the input graph.
result Reconstructs both geometry and topology of input graphs.
PLLay adds topological layers to deep learning models efficiently.
problem Efficiently incorporating topological features into deep learning models.
method Persistence landscapes for differentiable topological features.
result PLLay improves model learnability and robustness.
Neural network learns its size and structure during training.
problem Adapting neural network architecture to specific datasets.
method Flexible setup allowing neural network to learn size and topology during training.
result Trained networks achieve virtually identical performance and have learned optimal structure.
Study shows Hamiltonian diffeomorphisms form a connected component in C0-topology for most symplectic rational surfaces.
problem Understanding the C0-topology of symplectic diffeomorphisms on rational surfaces. method Combining techniques from symplectic mapping class groups and C0-symplectic topology, establishing C0-distance estimates. result Hamiltonian diffeomorphisms form a connected component in C0-topology for all but a few exceptions on rational surfaces. Novel tRSA combines geometry and topology for brain and model analysis.
problem Traditional RSA overlooks topological information in neural representations.
method Topological RSA (tRSA) using nonlinear monotonic transforms.
result Robust model comparisons and novel insights into neural computation.
Adaptive GPR-GNN optimizes node feature and topology learning.
problem Optimizing GNNs for both node features and graph topology, regardless of homophily or heterophily.
method Adaptive Universal Generalized PageRank (GPR) Graph Neural Network (GPR-GNN) that learns optimal GPR weights.
result Significant performance improvement on node classification tasks compared to state-of-the-art GNNs.
Estimates translator stability via topological features.
problem Quantifying stability of translators in geometric flows.
method Adapted Li-Tam theory to weighted settings, estimating nullity of stability operator.
result Quantitative index bounds for translators via topology.
We study stability properties of f-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the top…
Neural networks improve error correction in topological codes.
problem Finding optimal correction of errors in generic stabilizer codes is computationally hard.
method Systematic study of versatile neural-network decoders for topological codes.
result Neural decoders significantly improve error-correction threshold over leading efficient decoders.
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
New method reduces spatial graphs while preserving their topological features.
problem Finding a smaller spatial graph with the same structure.
method Topological spatial graph coarsening approach based on triangle-aware graph filtration.
result Significant reduction in graph size while preserving topological information.
Introduces directed diagrammatic reducibility with group and topological implications.
problem Diagrammatic reducibility in relative presentations.
method Adapting classical tools for diagrammatic reducibility to directed diagrammatic reducibility.
result Strong group theoretic and topological consequences of directed diagrammatic reducibility.
Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.
problem Uniform alignment of domains ignores topological structures.
method Uses a domain graph to encode adjacency and a novel graph discriminator.
result Empirically shows improved generalization and domain information incorporation.
Paper introduces a conformer-based system for streaming language identification in long-form speech.
problem Language identification in long-form audio.
method Conformer layers with attentive temporal pooling and domain adaptation.
result Conformer-based models significantly outperform LSTM and transformer models.
This work develops agents to learn generalizable policies for dynamic network environments.
problem Real-world network topologies change due to attackers, defenders, or system failures, leading to failures in adaptive ACD systems.
method Developing agents to learn generalizable policies across dynamic network environments.
result Agents can learn robust policies for dynamic network topologies and diverse attackers.
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus has the advantage that the number of evaluation points growths linearly with the…
FCM clustering adapts to persistence diagrams for topological data analysis.
problem Integrating topological data into machine learning workflows.
method Adapting Fuzzy c-Means to persistence diagrams.
result FCM clustering captures topological structure without additional processing.
Adaptive, sparse graphs improve learning performance.
problem Inappropriate kNN for varying sampling density or noise.
method Quadratically regularised optimal transport.
result Graphs outperform kNN in learning applications.
We use foams to give a topological construction of a rational link homology categorifying the slN link invariant, for N>3. To evaluate closed foams we use the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that for any link our homology is isomorphic to Khovanov and Rozansky's.
This paper proposes a new geometric model optimization method.
problem Building adaptive manifold models with dynamic geometry.
method Optimizing metric tensor field on a manifold with variational framework.
result Metric optimization yields models with greater expressive power than fixed geometry models.