The paper shows how coarse embeddings affect homological Dehn functions.
problem Characterizing groups with coarse embeddings into hyperbolic groups.
method Demonstrates a coarse embedding theorem for homological filling functions.
result Characterizes groups with coarse embeddings into hyperbolic groups of geometric dimension 2.
New embedding method in function spaces improves expressiveness.
problem Enhancing expressiveness in knowledge graph embeddings.
method Employing polynomial functions and neural networks with varying layer complexities.
result Improved expressiveness and more degrees of freedom in entity representation.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
problem Measuring place function similarity at fine spatial granularity.
method Trajectory embedding to reduce dimensions and measure similarity of place functions.
result Embedding similarity can be a metric proxy for place functions at fine spatial granularity.
Compact embeddings for invariant functions in metric-measure spaces.
problem Embedding functions with symmetry in metric-measure spaces.
method Analyzing H-invariant functions in compact metric-measure spaces, extending to Riemannian manifolds. result Obtained compact Sobolev embeddings for critical exponents.
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 framework infers multiple classes per image for one-shot learning.
problem Inferring multiple classes per image in one-shot learning.
method Compositional embedding framework with joint training of embedding and composition/query functions.
result Compositional embedding models outperform existing methods on various datasets.
Proves open Riemann surfaces can be embedded into 4D space.
problem Embedding open Riemann surfaces in lower dimensions.
method Proper harmonic embedding by harmonic functions.
result Reduces embedding dimension from previously known 5D to 4D.
We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.
problem Derivatives of manifold-valued functions are harder to approximate than vector-valued functions.
method Embed the manifold into a higher space, approximate the derivative of the vector-valued function, and project back.
result We provide error bounds for the approximation of manifold-valued function derivatives.
Study embeddings between Barron spaces with various activation functions, focusing on RePU.
problem Understanding the influence of activation functions on infinitely wide neural networks.
method Prove embeddings by constructing push-forward maps on measures representing functions.
result Barron spaces with RePU activation have a hierarchical structure similar to Sobolev spaces.
Motivated by manifold learning techniques, we give an explicit lower bound for how far a smoothly embedded compact submanifold in RN can move in a normal direction and remain an embedding. In addition, given a penalty function P:Emb(M,RN)→R on the space of embeddi…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function f, consistent estimators of the mean embedding of a random variable X lead to consistent estimators of the mean embedding of f(X). For Matérn ke…
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.
Ordinal embedding methods estimate perceptual scales from relative judgments.
problem Measuring subjective sensation using relative judgments.
method Ordinal embedding from machine learning applied to method of triads.
result Ordinal embedding allows estimating perceptual scales from few judgments, non-monotonous functions, and multi-dimensional scales.
Embedding 3-manifolds in R4 is obstructed by Heegaard curve complexes.
problem Obstructing embeddings of 3-manifolds into R4. method Using Heegaard curve complexes to find obstructions.
result An obstruction exists to realizing a Heegaard splitting as an embedding into R4. Improves manifold learning by identifying and fixing stuck points.
problem Local minima in nonlinear embedding methods lead to poor data structure visualization.
method Introduces a method to temporarily allow pressured points to use an extra dimension in the embedding space.
result Significantly improves the objective function value of existing methods even after getting stuck in a poor local minimum.
PGEL learns embeddings to diversify protein motifs while maintaining biological function.
problem Generating diverse protein structures while preserving biological function.
method Embedding learning framework that enhances motif diversity in a diffusion model's frozen denoiser.
result PGEL achieves greater structural diversity, better designability, and improved self-consistency compared to partial diffusion.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Bayesian deconditional embeddings solve complex function recovery.
problem Recovering original functions from conditional mean observations.
method Formalizes deconditional kernel mean embeddings as Bayesian inference, connects to task-transformed Gaussian processes.
result Establishes deconditional kernel means as posterior predictive mean, providing Bayesian interpretations and uncertainty.
We solve the vector embedding problem by minimizing total distortion under constraints.
problem Assigning representative vectors to items with similarity and dissimilarity constraints.
method Projected quasi-Newton method for MDE problems, scalable to large data sets.
result Our method provides principled ways to validate embeddings and scales to millions of items.
Label embedding (LE) is an important family of multi-label classification algorithms that digest the label information jointly for better performance. Different real-world applications evaluate performance by different cost functions of interest. Current LE algorithms often aim to optimize one specific cost function, b…
New KQEs improve probability metrics without mean function constraints.
problem Improving probability metrics without relying on mean function representations.
method Kernel quantile embeddings (KQEs) to construct new distances.
result KQEs offer a competitive alternative to MMD with near-linear cost.
PyKEEN 1.0 simplifies KGE model creation and optimization.
problem Training and evaluating knowledge graph embeddings (KGEs).
method Composes KGEMs with various interaction models, training approaches, and loss functions. Implements automatic memory optimization and extensive HPO functionalities.
result PyKEEN 1.0 streamlines KGE model creation and optimization.
Given a simplicial complex K, we consider several notions of geometric complexity of embeddings of K in a Euclidean space Rd: thickness, distortion, and refinement complexity (the minimal number of simplices needed for a PL embedding). We show that any n-complex with N simplices which topologically…
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.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. We prove that every proper n-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space R3n+6,1. By an "approximate isometric embedding" we mean an embedding which preserves the energy functional on a prescribed set of geodesics connecting a dense set of points.
New model for temporal KG completion using diachronic entity embeddings.
problem Temporal knowledge graph completion for incomplete KGs.
method Developed novel models by equipping static KG embedding models with a diachronic entity embedding function.
result Combining diachronic entity embeddings with SimplE results in superior temporal KG completion.
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. This paper tackles efficient optimization for nonlinear embeddings in similarity learning.
problem Learning similarity with nonlinear embeddings is challenging due to the large number of pairs.
method Detailed derivations and efficient optimization methods for nonlinear embeddings are developed.
result Efficient optimization methods for nonlinear embeddings are shown to be highly effective.
The paper proposes a new method to learn choice functions using Pareto-embeddings.
problem Learning subset choices from feature vectors.
method Embedding choice alternatives into a higher-dimensional utility space and identifying choice sets with Pareto-optimal points. Minimizing a differentiable loss function.
result The feasibility of learning a Pareto-embedding demonstrated on benchmark datasets.
This paper connects functional data analysis with machine learning techniques.
problem Lack of theoretical analysis for functional depths.
method Viewing functional depths as kernel mean embeddings in machine learning.
result Facilitates answers to open questions about functional depths.
Framework learns structural and functional brain network embeddings while preserving their properties.
problem Joint learning of structural and functional brain networks while preserving their intrinsic properties.
method Siamese community-preserving graph convolutional network (SCP-GCN) that learns from both structural and functional connectivity.
result Superior performance in neurological disorder analysis compared to existing methods.
Unified interpretation of softmax cross-entropy and negative sampling for knowledge graph embedding.
problem Lack of theoretical relationship between softmax cross-entropy and negative sampling loss functions in knowledge graph embedding.
method Used Bregman divergence to provide a unified interpretation of the two loss functions.
result Theoretical findings for fair comparison of softmax cross-entropy and negative sampling are derived.
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.
FPP creates interpretable 2D embeddings for high-dimensional data.
problem Discovering interpretable relationships in high-dimensional data.
method Function preserving projections (FPP) for scalable linear embeddings.
result FPP reveals non-linear patterns of user-selected response functions.
Improved similarity search in embeddings using InfoNCE loss.
problem Improving similarity search in embedding models trained by contrastive learning.
method Introduced a new continuity bound for InfoNCE loss via Gâteaux differentiation, preserving the averaging effect of negative samples.
result Demonstrated that the averaging effect of k negative samples in InfoNCE loss carries over to stabilisation of generalisation error as k grows. Gradient estimates for special harmonic functions on manifolds.
problem Estimating gradients of (p,V)-harmonic functions on Riemannian manifolds. method Using Moser iteration method, volume comparison theorem, and Sobolev embedding theorem.
result Explicit global gradient estimates for positive entire (p,V)-harmonic functions. CGNP embeds functional processes into latent vectors using graph neural networks.
problem Embedding and sampling functional processes over arbitrary domains.
method CGNP employs graph neural networks to embed and decode functional processes.
result CGNP effectively samples encoded functions over any domain.
Efficient RL in large POMDPs with latent determinism and embeddings.
problem Efficient reinforcement learning in large-scale POMDPs with latent states and observations.
method Conditional Hilbert space embeddings, linear optimal Q-function, deterministic latent transitions, gap assumption. result Computationally and statistically efficient algorithm for exact optimal policy.
Paper proposes DMGD for integrating outlier and community detection in graph embedding.
problem Outlier nodes affect graph embedding of regular nodes, especially in networks with multiple communities.
method DMGD integrates outlier and community detection with node embedding using multiclass graph description.
result DMGD detects outliers relative to their communities and achieves better node embedding compared to state-of-the-arts.
Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…
Embedding principle explains loss landscape of deep neural networks.
problem Understanding the structure of loss landscapes in deep neural networks.
method Proposed an embedding principle that critical points of narrower DNNs can be embedded to critical points of wider DNNs.
result Wide DNNs are often attracted by highly-degenerate critical points embedded from narrower DNNs.
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.
Embedded minimal surfaces of finite total curvature in R3 are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic embeddings in R3 of compact Riemann surfaces with finitely many punctures…
Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.
problem Establishing inequalities for radial functions on hyperbolic spaces without zero boundary conditions.
method Novel approach considering both bounded and unbounded domains, focusing on weighted Sobolev and Adams-Trudinger-Moser embeddings.
result Theorems 1.2, 1.3, and 1.4 for weighted Sobolev embedding theorems, and Theorems 1.5 and 1.6 for Adams-Trudinger-Moser type embedding theorems.
A new invariant captures geometric features of circle embeddings.
problem Capturing geometric features of circle embeddings invariantly.
method Chordal distance transform and persistent homology.
result Persistent homology of chordal distance transform is invariant.
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.
Paper introduces privacy-preserving few-shot learning for images.
problem Privacy risk in few-shot learning systems.
method Discrete embedding vectors and one-way hash functions.
result Achieves computational pan privacy without storing embeddings.