Improved molecular property prediction using WL embedding in GNNs.
problem Limited performance of GNNs in predicting molecular properties.
method Explored Weisfeiler-Lehman (WL) embedding to replace GNN layers, enhancing representability and performance.
result WL embedding consistently improves GNN performance across multiple datasets.
Introduces Hurewicz fibrations for embedding maps of orbifold charts.
problem No specific problem stated; focuses on new concept definition.
method Defines E-fibration embedding and studies its properties.
result Introduces and studies properties of E-fibration embedding.
New insights show embedding lengths correlate with semantic properties.
problem Contrastive embedding norms ignore embedding magnitudes but correlate with semantic properties.
method Formal theoretical framework and analysis of optimization dynamics.
result Embedding lengths encode semantic information as a byproduct of training.
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
This paper studies node embeddings of networks, revealing their geometric properties.
problem Understanding the geometric properties of node embeddings in random networks.
method Characterization of ergodic limits, generalization, and convex relaxations of random walk node embedding objectives.
result The optimal node embedding Grammians have rank 1 for a nuclear norm relaxation of the non-randomized objective.
Embedding Projector visualizes and interprets embeddings interactively.
problem Exploring properties of embeddings in machine learning.
method Interactive visualization and interpretation tool for embeddings.
result Interactive exploration of embedding properties.
We consider the following properties of compact oriented irreducible graph-manifolds: to contain a π1-injective surface (immersed, virtually embedded or embedded), be (virtually) fibered over S1, and to carry a metric of nonpositive sectional curvature. It turns out that all these properties can be described from…
Examines properties of negatively curved 3-manifolds and their embeddings, introduces Cross Curvature Flow.
problem Understanding negatively curved three-manifolds and their embeddings.
method Reviews Cross Curvature Flow as a tool, examines rigidity properties, reviews embeddings into Minkowski space.
result Fixed Einstein volume solutions are integrable solutions, answering a question posed by Chow and Hamilton.
This paper studies surfaces with a special lift property.
problem Geometry of surfaces with a specific lift property.
method Generalizes previous results by Bernstein and Tinaglia.
result Leaves of minimal laminations satisfy the generalised simple lift property.
Characterizes graphs with leveled embeddings and introduces new graph invariants.
problem Understanding the properties of leveled embeddings in spatial graphs.
method Characterization of graphs with leveled embeddings, introduction of new invariants.
result Characterization of graphs with low level number and determination of specific invariants for complete graphs and complete bipartite graphs.
Graph products inherit Morse local-to-global property from their components.
problem Generalizing local-to-global property to graph products of infinite groups.
method Generalizing maximization procedure for relatively hierarchically hyperbolic groups and showing stable embeddings.
result Graph products of infinite Morse local-to-global groups have the Morse local-to-global property.
New research shows graph embeddings fail to capture key network properties.
problem Graph embeddings fail to capture salient properties of complex networks.
method Mathematical proof and empirical study of various embedding techniques.
result Any successful graph embedding must have a rank nearly linear in the number of vertices.
New obstruction found for embedding Riemannian manifolds into Euclidean spaces.
problem Embedding Riemannian manifolds into Euclidean spaces with specific conditions.
method Motivated by incompressible Euler equations, a dynamical-topological obstruction is derived.
result Nontrivial first real homology and trivial center of fundamental group imply embedding violation.
Event2vec learns object embeddings in HINs by considering both relation properties and quantities.
problem Ignoring relation properties in existing NRL methods for HINs.
method Event2vec uses events to represent relations and defines event-driven proximities to measure object relevance.
result Event2vec preserves event-driven proximities in the embedding space and outperforms state-of-the-art methods.
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The…
This paper tackles scale-free networks by preserving their heavy-tailed vertex degree distribution.
problem Preserving the scale-free property in network embeddings.
method Proposes a 'degree penalty' principle to design algorithms that preserve the heavy-tailed degree distribution of scale-free networks.
result Our algorithms reconstruct the heavy-tailed degree distribution and outperform state-of-the-art models in network mining tasks.
Graph embedding techniques convert graph data into vectors to preserve graph properties.
problem Handling high-dimensional irregular graph data.
method Various graph embedding techniques to convert graph data into low-dimensional vectors.
result Evaluation of state-of-the-art methods on small and large datasets.
Study geodesic properties of time series data using Wasserstein metric.
problem Modeling nonlinear time series with transport-based metrics.
method Generalized Wasserstein metric and signed cumulative distribution transforms.
result Geodesic properties provide added interpretability and robustness in time series classifiers.
Proposes a novel approach using vector cross product to preserve directional edges in directed graphs.
problem Preserving directional edges in directed graphs for tasks like link prediction and node recommendation.
method Integrates the non-commutative property of vector cross product into a Siamese neural network to learn N-dimensional embeddings.
result Low-dimensional embeddings effectively preserve directional properties and outperform state-of-the-art methods.
Study on embedding properties of Riemannian manifolds with specific geometric constraints.
problem Embedding Riemannian manifolds with certain geometric properties into Euclidean spaces.
method Utilizing a known trick to find embeddings with specific dimensions.
result Existence of isometric embeddings with specified dimensions for Riemannian manifolds.
Study optimal Skorokhod embedding problem for Brownian motion.
problem Optimizing stopping times for Brownian motion with given distribution.
method Weak density of stopping times, dual optimization, compactness property.
result Existence of dual solutions and absence of duality gap for irregular reward functions.
Fewer obstructions for small graphs in knotless embedding.
problem Finite obstructions for knotless embedding of small graphs.
method Analysis of graph minor obstructions and knotless embedding.
result There are only three obstructions for size 23 graphs, significantly fewer than previously known.
Paper develops heavy-tailed embeddings for better text classification and augmentation.
problem Improving text classification, especially for extreme values.
method Develops heavy-tailed embeddings using multivariate extreme value theory and introduces a scale-invariant classifier.
result The classifier outperforms baselines and generates meaningful augmented text.
In this paper we give two examples of sequences of embedded minimal planar domains in R3 which converge to singular laminations of R3. In contrast with the situation for embedded minimal disks, these examples do not arise from complete embedded minimal planar domains and highlight some of the su…
This paper explores sentence vector properties for automatic summarization.
problem Understanding the internal structure and properties of sentence vectors.
method Compositional sentence vector representations using artificial neural networks.
result Cosine similarity correlates with sentence importance and can identify gaps in summaries.
The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on CPn and parallel plurimean curvature. result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
In this paper, by constructing area-nonincreasing retractions, we prove area-minimizing properties of some cones over minimal embeddings of R-spaces.
For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is equivalent to a strong equivariant immersion.
New subgroups found in CAT(0) groups with exotic finiteness properties.
problem Constructing subgroups with specific finiteness properties.
method Building subgroups L of CAT(0) groups G with tailored finiteness types. result Found subgroups L of finiteness type Fn−1 but not Fn. Given a finite cover f:tilde{G} \to G and an embedding of tilde{G} in the plane, Negami conjectures that G embeds in P^2. Negami proved this conjecture for regular covers. In this paper we define two properties (Propserties V and E), depending on the cover tilde{G} and its embedding into S^2, and generalize Negami's re…
Study on exotic smooth embeddings of surfaces in 4-manifolds, revealing different properties and complexities.
problem Understanding exotic smooth embeddings of surfaces in 4-manifolds.
method Analyzing smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli.
result Exotic planes and annuli exhibit radically different properties, with one class being simple enough to draw explicit level diagrams.
Study conic singular manifolds, proving Lipschitz normal embedding.
problem Understanding metric properties of conic singular manifolds.
method Analyzing interplay between conic and asymptotically conic behavior.
result Proves Lipschitz normal embedding for conic singular sub-manifolds.
Machine learning algorithms are optimized to model statistical properties of the training data. If the input data reflects stereotypes and biases of the broader society, then the output of the learning algorithm also captures these stereotypes. In this paper, we initiate the study of gender stereotypes in {\em word emb…
The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fáry's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest pa…
We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two component link with lk(A,L) = k2^r, k not 0, a non-split n-component link where all l…
The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.
BIGUE algorithm provides credible intervals for hyperbolic network embeddings.
problem Uncertainty in hyperbolic network embeddings.
method Markov chain Monte Carlo (MCMC) algorithm for Bayesian hyperbolic random graph model.
result Samples from the posterior distribution provide credible intervals for hyperbolic coordinates and network properties.
LCNs use Lovasz embeddings to capture global graph properties.
problem Semi-supervised learning on graph data.
method LCNs use Lovasz embeddings to incorporate global graph properties.
result LCNs outperform GCNs on various graph models and real-world datasets.
A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…
CNEs improve network embeddings by adding structural information.
problem Hard embedding of certain networks due to structural properties.
method Bayesian approach to create embeddings that maximize information with given structural properties.
result CNEs outperform state-of-the-art methods in link prediction and multi-label classification.
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
problem Organizing and understanding the complex folding patterns of RNA secondary structures.
method Geometric scattering autoencoder (GSAE) network for learning graph embeddings.
result GSAE accurately reflects bistable RNA structures and can sample new folding trajectories.
DeepWalk embeddings converge on SBM graphs, recovering cluster structure.
problem Theoretical guarantees for DeepWalk embeddings on complex graphs.
method Solving a nonconvex optimization problem using random walks.
result DeepWalk embeddings on SBM graphs recover cluster structure with high probability.
Paper improves data embeddings with Lagrange duality.
problem Near isometric orthogonal embeddings for data points.
method Formulated as non-convex optimization, used Lagrange duality for relaxation, and provided a polynomial time algorithm.
result Achieved better approximation guarantees and lower distortion compared to baselines.
Paper explores RKHS properties for derivative and integral operators.
problem Establishing sufficient conditions for reproducing property in RKHS.
method Establishing reproducing property for combinations of composition operators.
result Provides framework for regularized learning algorithms involving function values, gradients, or operators.
Study shows intersections of stable subgroups have finite properties.
problem Understanding intersections of stable subgroups in finitely generated groups.
method Analyzing intersections of conjugates and extending quasimorphisms.
result Finite families of quasimorphisms can be simultaneously extended to the ambient group.
The blind application of machine learning runs the risk of amplifying biases present in data. Such a danger is facing us with word embedding, a popular framework to represent text data as vectors which has been used in many machine learning and natural language processing tasks. We show that even word embeddings traine…
Investigates neural codes and their embeddings, proving conjectures and introducing new code types.
problem Analyzing neural codes and their embedding dimensions.
method Combinatorial, topological, and algebraic analysis; proving conjectures; introducing new neural code types.
result Proves conjectures about neural codes and their embeddings, introduces new code types.
PanRep learns universal node embeddings for heterogeneous graphs.
problem Learning universal node embeddings for heterogeneous graphs.
method Graph Neural Network (GNN) model with four decoders capturing different properties.
result PanRep outperforms unsupervised and supervised methods in node classification and link prediction.