Derives conditions for embedding smooth surfaces into higher dimensions.
problem Conditions for embedding smooth surfaces into higher dimensions.
method Derives necessary and sufficient conditions for 1-quasiconformal parameterization.
result Liouville theorem does not extend to embeddings of domains into higher dimensions.
For the result on 1-quasiconformal maps, see the paper by Cowling and Ottazzi. The result on quasiconformal maps on Carnot groups with reducible first layer will appear in a forthcoming paper by Enrico Le Donne and Xiangdong Xie.
We characterize the rigidity of Carnot groups in the class of C2 contact maps in terms of complex characteristics. Furthermore, we obtain a Liouville type theorem for Carnot groups which states that 1-quasiconformal maps form finite dimensional Lie groups.
L. Capogna and M. Cowling showed that if φ is 1-quasiconformal on an open subset of a Carnot group G, then composition with φ preserves Q-harmonic functions, where Q denotes the homogeneous dimension of G. Then they combine this with a regularity theorem for Q-harmonic functions to show that φ is in fact $C^\inft…
Equivalence of conformal maps proved in sub-Riemannian manifolds.
problem Equivalence of conformal maps between sub-Riemannian manifolds.
method Regularity theory for subelliptic p-Laplacian operators, sub-Riemannian p-harmonic coordinates, propagation of regularity.
result 1-quasiconformal maps are smooth on contact manifolds.
The Myers-Steenrod theorem is extended to Finsler manifolds with low regularity.
problem Extending the Myers-Steenrod theorem to Finsler manifolds with minimal regularity.
method Reduction of Finslerian problems to Riemannian ones using the Binet-Legendre metric.
result Isometries between Ck,α-smooth Finsler metrics are diffeomorphisms of class Ck+1,α. Equivalence of quasiregular mappings on subRiemannian manifolds proven.
problem Equivalence of quasiregular mappings on subRiemannian manifolds.
method New Popp extensions of horizontal metrics and distortion estimates.
result All quasiregular mappings are equivalent with precise dependencies.
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.
Disk Embeddings tackle embedding DAGs with exponential growth.
problem Embedding DAGs with exponentially increasing ancestors and descendants.
method Disk Embeddings framework for quasi-metric spaces, including Hyperbolic Disk Embeddings.
result Disk Embeddings outperform existing methods in complex DAGs.
Proposes QQE for transforming and embedding data distributions.
problem Transforming and embedding data distributions for better representation or visualization.
method Quantile-Quantile Embedding (QQE) using quantile-quantile plot concept.
result QQE allows for better discrimination of classes in some cases.
Dynamic embeddings capture evolving word meanings over time.
problem Capturing how word meanings change over time in historical texts.
method Developed dynamic Bernoulli embeddings based on exponential family embeddings.
result Dynamic embeddings provide better fits and reveal interesting language change patterns.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
problem Embedding maps in higher dimensions without self-intersections.
method Lifting maps to embeddings in product spaces.
result Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
A new embedding structure, res-embedding, improves deep CTR models by enhancing generalization performance.
problem Deep CTR models often suffer from poor generalization performance due to learning of embedding parameters.
method Developed a res-embedding structure that combines a central embedding vector from an item-based interest graph with a residual embedding vector.
result Empirical evaluation shows significant improvement in model performance using the res-embedding structure.
New embeddings for manifolds using heat kernels.
problem Constructing canonical conformal embeddings for manifolds.
method Employing heat kernel embedding from Bérard-Besson-Gallot'94 to find canonical conformal embeddings.
result Intrinsic construction of canonical conformal embeddings with dimensions growing exponentially with t. Binary embeddings speed up graph data retrieval.
problem Efficiently retrieving graphical data.
method Binary valued embeddings modeled as coin flips with varying bias, optimized using continuous optimization techniques.
result Binary embeddings outperform other methods on various datasets.
Introduces PELP for graph-enhanced word embeddings.
problem Combining graph side-information into static word embeddings.
method Probabilistic embeddings using Laplacian priors.
result Unified and flexible approach to various embedding methods.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Parallelizes graph embedding for large graphs.
problem Large graphs make existing graph embedding techniques inefficient.
method Distributed parallel computation framework using a cluster of compute nodes.
result Parallel computation scales well and maintains embedding quality.
dynnode2vec embeds dynamic networks efficiently.
problem Capturing evolving patterns in large dynamic networks.
method dynnode2vec: a random walk based method initialized with previous embedding vectors.
result Demonstrates advantages over static methods on large dynamic network datasets.
Proposes cone embedding for better graph hierarchical structure representation.
problem Lack of natural and interpretable hierarchical indicators in graph embeddings.
method Metric cone embedding method to capture hierarchical structure.
result Extracts hierarchical structure from other graph embedding outputs.
Improves machine learning performance with domain-specific embeddings.
problem Tuning word embeddings for specific use cases and domains.
method Combines multiple domain-specific embeddings using a ranking function and dimensionality reduction.
result Effective domain-specific embeddings improve machine learning performance.
Classifies linear embeddings of grassmannians and ind-grassmannians.
problem Understanding linear embeddings of grassmannians and ind-grassmannians.
method Classification through isomorphism of Picard groups and direct limits.
result Most linear embeddings of grassmannians are equivariant.
DANE adapts network embeddings across multiple domains.
problem Learning embeddings for multiple networks without transferability.
method Graph Convolutional Network with adversarial learning.
result DANE achieves superior performance in cross-network domain adaptation.
BC-Aligner maintains backward compatibility of embeddings after frequent updates.
problem Updating embeddings without requiring consumer teams to retrain their models.
method Learning backward compatible embeddings through BC-Aligner.
result BC-Aligner maintains backward compatibility with existing unintended tasks after multiple model version updates.
Survey on embedding techniques in source code.
problem Applying word embedding techniques to source code.
method Collection and categorization of articles from related work and scholarly searches.
result Word embedding has been successfully applied to various granularities of source code.
Unified framework for word embedding models using noise examples.
problem Improving word embedding models with negative sampling.
method Formulated a Word-Context Classification (WCC) framework that generalizes SkipGram word embedding models.
result The best noise distribution is the data distribution, improving both performance and training speed.
Embedding calculus proves convergence for surfaces.
problem Proving convergence of embedding calculus for surfaces.
method Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two.
result Relates Johnson filtration of mapping class group to embedding calculus.
Models use embeddings and attention for better claim severity prediction.
problem Improving predictive modeling of claim severity with categorical data.
method Developed neural networks and attention-based architectures with embeddings.
result Attention-based models enhance predictive performance with contextual augmentation.
A fast graph embedding method for large graphs.
problem Efficiently embedding large graphs for various applications.
method One-hot graph encoder embedding with linear complexity.
result Graph encoder embedding is approximately normally distributed and converges to its mean.
The paper investigates if graph embeddings capture key topological features.
problem Exploring if graph embeddings approximate traditional vertex level graph features.
method Predicting known topological features from graph embeddings using supervised and unsupervised methods.
result Several topological features are approximated by the embedding space, providing insight into how graph embeddings function.
Paper proposes a new word embedding method optimizing word similarity.
problem Optimizing word similarity in embedding space.
method Two-step random walks between words via topics to learn an optimal embedding simplex.
result Our method outperforms existing approaches in various queries.
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.
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.
Proves uniqueness of embedding complex manifold into infinite-dimensional space.
problem Balanced embedding of non-compact complex manifold into infinite-dimensional projective space.
method Fine estimates of asymptotics of a balanced embedding.
result Uniqueness of embedding proven.
The paper defines invariants for almost graph embeddings and explores their properties.
problem Understanding the properties and limitations of almost graph embeddings in the plane.
method Introducing and analyzing integer invariants (winding number, Wu numbers) for almost embeddings.
result Some values of invariants are realizable for almost embeddings but not for embeddings.
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
This work analyzes PPR-based node embeddings and their topological information.
problem Understanding and interpreting PPR-based node embeddings.
method Unified framework and two methods for topology recovery.
result PPR-based embeddings maintain more topological information than random walk-based embeddings.
The paper proves embedding theorems for CR manifolds using Fourier-Szegő kernels.
problem Embedding CR manifolds into complex spaces.
method Fourier-Szegő kernels and equivariant Kodaira embedding theorems.
result Full asymptotic expansions of weighted Fourier-Szegő kernels for CR sections.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
problem Finding a surface embedding for general spatial graphs is not always possible.
method Define leveled property, decompose graph into subgraphs, and construct surface.
result For leveled spatial graphs with a small number of levels, a surface can always be found.
Proves embedding of metric spaces into Lorentzian space.
problem Embedding length metric spaces isometrically.
method Proves approximate isometric embedding into Lorentzian space.
result Every proper n-dimensional length metric space can be embedded approximately.
Proposes spherical text embedding for better directional similarity.
problem Directional similarity is more effective but unsupervised text embeddings are typically learned in Euclidean space.
method Develops a spherical generative model and an efficient optimization algorithm for unsupervised word and paragraph embeddings.
result Achieves state-of-the-art performances on various text embedding tasks.
Long spacelike embeddings can be approximated by isometric ones.
problem Approximating long embeddings to isometric embeddings in Lorentzian spaces.
method Proving approximation by constructing C1 isometric embeddings. result Long spacelike embeddings can be C0-approximated by C1 isometric embeddings. A {\it wrinkled embedding} f:Vn→Wm is a topological embedding which is a smooth embedding everywhere on V except a set of (n−1)-dimensional spheres, where f has cuspidal corners. In this paper we prove that any rotation of the tangent plane field TV⊂TW of a {\it smoothly embedded} submanifold $V\s…
Compositional Network Embedding learns node embeddings from node features.
problem Cold-start problem and lack of robustness to noise in existing network embedding methods.
method Generative framework that combines node attribute embeddings through a graph-based loss.
result Effectiveness and generalization of compositional network embeddings, especially on unseen nodes.
Embeddings between multicurve graphs induced by surface embeddings.
problem Understanding how surfaces can be mapped into each other.
method Analyzing k-multicurve graphs and their embeddings.
result Simplicial embeddings between multicurve graphs are induced by π1-injective surface embeddings. Paper proposes a new approach to unify and compare knowledge graph embedding methods.
problem Lack of understanding and comparison of existing knowledge graph embedding methods.
method Introduces a multi-embedding interaction mechanism to unify and generalize existing models.
result Proposes a new multi-embedding model based on quaternion algebra.
Researchers explain how W2V and GloVe embeddings work and why they are useful.
problem Lack of theoretical understanding of W2V and GloVe embeddings.
method Theoretical analysis of PMI vectors and their interactions.
result W2V and GloVe embeddings capture semantic relationships like similarity and paraphrasing.
Saec compresses recommendation system embeddings by clustering similar features.
problem Large embedding matrix in recommendation systems consumes excessive memory.
method Saec clusters similar features within a field to reduce embedding matrix size.
result Saec reduces embedding size by ~27x with no performance loss.