相关论文: Generalization Error Bound for Hyperbolic Ordinal …
Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view…
Learning the intrinsic dimensionality of subjective perceptual spaces such as taste, smell, or aesthetics from ordinal data is a challenging problem. We introduce LORE (Low Rank Ordinal Embedding), a scalable framework that jointly learns…
The hyperbolic lattice point problem asks to estimate the size of the orbit $\Gamma z$ inside a hyperbolic disk of radius $\cosh^{-1}(X/2)$ for $\Gamma$ a discrete subgroup of $\hbox{PSL}_2(R)$. Selberg proved the estimate $O(X^{2/3})$ for…
Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different…
Bayesian Optimization (BO) in high-dimensional spaces remains fundamentally limited by the curse of dimensionality and the rigidity of global low-dimensional assumptions. While Random EMbedding Bayesian Optimization (REMBO) mitigates this…
Given an elliptic curve $E$ defined over $\mathbb{Q}$ without complex multiplication, we provide an explicit sharp bound on the index of the image of the adelic representation $\rho_E$. In particular, if $\operatorname{h}_{\mathcal{F}}(E)$…
We discuss generalizations of the well-known theorem of Hilbert that there is no complete isometric immersion of the hyperbolic plane into Euclidean 3-space. We show that this problem is expressed very naturally as the question of the…
Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…
The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Ast\'erisque {\bf 270} (2001), dealt with geometric properties of metric spaces. In this…
Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…
Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks.…
Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
We consider the problem of multi-label classification where the labels lie in a hierarchy. However, unlike most existing works in hierarchical multi-label classification, we do not assume that the label-hierarchy is known. Encouraged by the…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…