The curve graph and related graphs are hyperbolic and have quasi-tree fibers.
problem Understanding the structure of the curve graph and related graphs.
method Analyzing a sequence of graphs with Lipschitz maps and proving hyperbolicity and quasi-tree properties.
result The graphs in the sequence are hyperbolic and have quasi-tree fibers, leading to bounds on asymptotic dimension and acylindrical actions.
Grid homology theory for spatial graphs extends skein sequence.
problem No specific problem stated; focuses on extending a sequence.
method Defined grid homology theory for spatial graphs and extended skein sequence.
result Skein exact sequence extended to grid homology for spatial graphs.
A new method for fast graph embedding using diffusion graphs.
problem Efficiently generating graph embeddings for large networks.
method Diffusion graphs for rapid vertex sequence generation.
result Improved accuracy and performance with higher edge density.
Paper proposes AR model for graph sequences.
problem Predicting sequences of graphs with variable topology.
method Formalizes AR model for graphs using GNN to learn and predict next graph.
result Significantly better performance on synthetic graph generation problems.
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed 4-regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface. result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
AutoGraph uses transformers to efficiently generate graphs as sequences.
problem Efficiently generating large, sparse graphs without expensive node features.
method Flattening graphs into sequences and using decoder-only transformers.
result AutoGraph achieves state-of-the-art performance on synthetic and molecular benchmarks.
The celebrated Sequence to Sequence learning (Seq2Seq) technique and its numerous variants achieve excellent performance on many tasks. However, many machine learning tasks have inputs naturally represented as graphs; existing Seq2Seq models face a significant challenge in achieving accurate conversion from graph form …
SENSE enhances node sequences in graphs using vector embeddings.
problem Efficiently capturing graph node sequences for applications.
method SENSE-S learns node embeddings and composes them for sequences, preserving node order.
result SENSE-S increases multi-label classification and link-prediction accuracy by up to 50% and 78% respectively.
Summarization of long sequences into a concise statement is a core problem in natural language processing, requiring non-trivial understanding of the input. Based on the promising results of graph neural networks on highly structured data, we develop a framework to extend existing sequence encoders with a graph compone…
Learned factor graphs improve inference from time sequences using neural networks.
problem Inference from time sequences with limited labeled data.
method Combines model-based algorithms and data-driven ML tools for stationary time sequences.
result Learned factor graphs can accurately infer from small training sets.
Novel graph neural network combines random walks with local message passing.
problem Graph neural networks struggle with long-range dependencies.
method Combines random walks with local message passing in a novel architecture.
result Significant performance improvements on graph benchmarks.
System uses neural networks to prove program equivalence via rewrite rules.
problem Proving equivalence between two dataflow graphs.
method Developed a graph-to-sequence neural network trained on example generation to find semantics-preserving rewrite rules.
result System correctly outputs a rewrite sequence for 96% of program pairs, proving equivalence.
Predicts node sequences in graphs using multi-order network models.
problem Predicting sequences of node traversals in graphs.
method Combines multiple higher-order network models into a multi-order model, fitting and selecting the optimal maximum order.
result Outperforms state-of-the-art algorithms for next-element and full sequence prediction.
Graph Hawkes Neural Network forecasts evolving graph sequences.
problem Modeling dynamic graph sequences with complex event types.
method Generalized Hawkes process to neural network, capturing complex event impacts.
result Effective at predicting future events in evolving graph sequences.
Graph ConvNet improves ncRNA classification accuracy.
problem Classifying non-coding RNA sequences into families.
method Graph Convolutional Network model trained on raw RNA graphs.
result 85.73% accuracy and 85.61% F1-score over 13 classes.
DynGraph2Seq predicts health stages from user activity graphs in online forums.
problem Predicting health stages from changing user activities in online forums.
method Formulated user activities as dynamic graphs, used DynGraph2Seq model with hierarchical attention.
result Demonstrated effectiveness and interpretability of DynGraph2Seq.
Contradiction graphs reveal VC dimension threshold.
problem Determining VC dimension of concept classes.
method Study contradiction graphs of binary concept classes.
result Single contradiction graph Gm(H) determines VC dimension. Graph theory connects automorphisms to cohomology.
problem Understanding automorphism actions on graph cohomology.
method Graph-theoretical interpretation of de Rham cohomology.
result Proves graph analogues of differential geometry results.
GNL addresses dynamic network regression by learning dynamic graph structures and capturing sequence information.
problem Dynamic network regression of multiple inter-connected data entities.
method Graph Neural Lasso (GNL) using gated diffusive units and attention mechanism.
result GNL outperforms existing methods in dynamic network regression tasks.
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is previous work on Graph Neural Networks (Scarselli et al., 2009), which we modif…
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in v…
Graph WaveNet models spatial-temporal graphs by learning hidden dependencies and long sequences.
problem Capturing hidden spatial dependencies and long-range temporal sequences in graphs.
method Graph WaveNet integrates adaptive dependency matrix learning and stacked dilated 1D convolution.
result Graph WaveNet outperforms existing methods on public traffic network datasets.
Develops a tensor network framework to reduce RNN complexity for high-dimensional sequence modeling.
problem Exponential parameter growth in RNNs for large multidimensional data.
method Embeds a multi-linear graph filter in a tensor network architecture to approximate RNN hidden states.
result Demonstrates superior performance and reduced complexity compared to traditional RNNs.
Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding …
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Classifies intrinsically linked tournaments by their score sequences.
problem Classifying intrinsically linked tournaments using their score sequences.
method Examining the score sequences of tournaments and identifying linkless sequences.
result The vast majority of score sequences for 8-vertex tournaments are linkless.
In this thesis we describe how to estimate the distance spanned in the pants graph by a train track splitting sequence on a surface, up to multiplicative and additive constants. If some moderate assumptions on a splitting sequence are satisfied, each vertex set of a train track in it will represent a vertex of a graph …
DGE learns event representations from image sequences without manual annotations.
problem Data hunger and domain adaptation issues in self-supervised learning for temporal segmentation.
method Dynamic Graph Embedding (DGE) learns event representations by iteratively updating a graph and its embedding.
result DGE achieves robust temporal segmentation on benchmark datasets, outperforming state-of-the-art methods.
Modeling and estimating dynamic graphs from binary pattern sequences.
problem Extracting dominant correlation structures from time-dependent binary patterns.
method State-space model of an Ising-type network composed of multiple undirected graphs, sequential Bayes algorithm.
result The method outperforms traditional methods in uncovering overlapping graphs and estimating dynamics of weights.
A method to generate long-range human actions by leveraging graph convolutional networks and self-attention.
problem Generating long-range skeleton-based human actions is challenging due to small frame deviations.
method Proposes a variant of GCNs with self-attention to adaptively sparsify action graphs and capture structure information.
result Extensive experiments show superior performance compared to existing methods on human action datasets.
Although the computational and statistical trade-off for modeling single graphs, for instance, using block models is relatively well understood, extending such results to sequences of graphs has proven to be difficult. In this work, we take a step in this direction by proposing two models for graph sequences that captu…
We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheimer-Mrowka's instanton invariants J♯ and I♯ for spatial webs by two spectral sequences. As an application of the spectral seq…
Spacetimeformer learns spatiotemporal relationships from data alone.
problem Forecasting multivariate time series with distinct spatial relationships.
method Transformers with dynamic graph connections learning interactions between space, time, and value.
result Competitive results on various time series prediction benchmarks.
This paper clarifies vine copula structures using graph and matrix representations.
problem Ambiguity in vine copula representations in literature.
method Graph and matrix representations to clarify vine structures, including cherry and chordal sequences.
result A unique matrix representation of vine structures when given a perfect elimination ordering.
The paper studies algebraic integer relations and sequences converging to 4.
problem Investigating algebraic integer relations and convergence of sequences.
method Constructing a generalized Farey graph for the subgroup Gα and analyzing its properties. result A sequence of algebraic integers converges to 4, each corresponding to a non-free group of rank 2.
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is of an exponential complexity with respect to t…
Let Sg,p denote the genus g orientable surface with p punctures. We show that nested train track sequences constitute O((g,p)2)-quasiconvex subsets of the curve graph, effectivizing a theorem of Masur and Minsky. As a consequence, the genus g disk set is O(g2)-quasiconvex. We also show that splitti…
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We prese…
In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the independence model induced by another chain graph G, then (i) G can be transformed into H …
New method enhances graph neural networks using contractions and hourglass persistence.
problem Limitations of traditional persistent homology in graph neural networks.
method Hourglass Persistence, Contraction Homology, contractions as a topological operation.
result Hourglass Persistence boosts expressivity, learnability, and stability in graph representation learning.
MEGAN models chemical reactions as graph edits, improving synthesis planning.
problem Generating and predicting chemical reactions under constraints.
method End-to-end encoder-decoder neural model inspired by arrow pushing formalism.
result State-of-the-art accuracy in standard benchmarks for retrosynthesis prediction.
Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to cover a large class of applications, we consider the general family of attribute…
We embed arbitrary groups into regular graphs with prescribed automorphisms.
problem Embedding arbitrary groups into regular graphs with specific automorphisms.
method Constructing regular graphs with strong embeddings and automorphism groups isomorphic to any given finite group.
result For every d≥3 and every finite group G, there exists a d-regular graph Γ with a strong embedding β such that Aut(Γ)≅Aut(β(Γ))≅G. Multistep traffic forecasting on road networks is a crucial task in successful intelligent transportation system applications. To capture the complex non-stationary temporal dynamics and spatial dependency in multistep traffic-condition prediction, we propose a novel deep learning framework named attention graph convol…
Study homology of periodic cell complexes using quotient spaces and spectral sequences.
problem Quantifying homology in periodic cell complexes.
method Finite representation of periodic cell complexes, Mayer-Vietoris spectral sequence.
result Full recovery of homology generators for d-periodic graphs. Graph-based NAS improves sample efficiency in architecture design.
problem Current NAS search spaces are static sequences, limiting expressiveness.
method Proposed graph-based search space with vertices and edges for iterative and branching decisions.
result Graph representation improves sample efficiency in architecture design.
New model generates graphs with tighter likelihood bounds and better quality.
problem Intractable likelihood of autoregressive graph models.
method Derive exact joint probability, approximate node orderings, variational inference.
result Lower bound on log-likelihood is significantly tighter than previous methods.
GGP models multivariate time series with latent sub-sequences for diverse behaviors.
problem Modeling multivariate time series with diverse behaviors and patterns.
method Graph Gamma Process (GGP) linear dynamical systems with latent sub-sequences.
result GGP models exhibit good predictive performance and reveal interpretable latent patterns.