Related papers: Simplicial Complex Representation Learning
An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent…
Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have employed strings, fingerprints, global…
In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…
In continual and lifelong learning, good representation learning can help increase performance and reduce sample complexity when learning new tasks. There is evidence that representations do not suffer from "catastrophic forgetting" even in…
The complexity of visual stimuli plays an important role in many cognitive phenomena, including attention, engagement, memorability, time perception and aesthetic evaluation. Despite its importance, complexity is poorly understood and…
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have been invented. In this paper, we give some algorithms to…
Objects we interact with and manipulate often share similar parts, such as handles, that allow us to transfer our actions flexibly due to their shared functionality. This work addresses the problem of transferring a grasp experience or a…
Recent works on representation learning for Knowledge Graphs have moved beyond the problem of link prediction, to answering queries of an arbitrary structure. Existing methods are based on ad-hoc mechanisms that require training with a…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
Visual recognition tasks are often limited to dealing with a small subset of classes simply because the labels for the remaining classes are unavailable. We are interested in identifying novel concepts in a dataset through representation…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…
Volumetric design, also called massing design, is the first and critical step in professional building design which is sequential in nature. As the volumetric design process requires careful design decisions and iterative adjustments, the…
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
Since about 100 years ago, to learn the intrinsic structure of data, many representation learning approaches have been proposed, including both linear ones and nonlinear ones, supervised ones and unsupervised ones. Particularly, deep…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from…
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…