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We introduce a novel latent vector space model that jointly learns the latent representations of words, e-commerce products and a mapping between the two without the need for explicit annotations. The power of the model lies in its ability…
Since Knowledge Graphs (KGs) contain rich semantic information, recently there has been an influx of KG-enhanced recommendation methods. Most of existing methods are entirely designed based on euclidean space without considering curvature.…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…
Learning meaningful abstract models of Markov Decision Processes (MDPs) is crucial for improving generalization from limited data. In this work, we show how geometric priors can be imposed on the low-dimensional representation manifold of a…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…
We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…
Knowledge Graphs (KGs) enhance recommender systems but face challenges from inherent noise, sparsity, and Euclidean geometry's inadequacy for complex relational structures, critically impairing representation learning, especially for…
Molecules have seemed like a natural fit to deep learning's tendency to handle a complex structure through representation learning, given enough data. However, this often continuous representation is not natural for understanding chemical…
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…
In past research on self-supervised learning for image classification, the use of rotation as an augmentation has been common. However, relying solely on rotation as a self-supervised transformation can limit the ability of the model to…
In this paper, we proposes the construction methods of sliced space-filling design when the quantitative factors are mixture components. Leveraging the representative points framework for distribution and energy distance decomposition…
Current 3D-aware pretraining methods for embodied perception and manipulation are largely built on differentiable rendering frameworks, producing either fully implicit neural fields or fully explicit geometric primitives. Implicit…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
Physical data are representations of the fundamental laws governing the Universe, hiding complex compositional structures often well captured by hierarchical graphs. Hyperbolic spaces are endowed with a non-Euclidean geometry that naturally…
This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…