More Like this

1. Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones

   Bai, J; Ying, R; Ren, H; Leskovec, J (December 2021, Advances in neural information processing systems)

   Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning. However, current KG embeddings can model only a single global hierarchy (single global partial ordering) and fail to model multiple heterogeneous hierarchies that exist in a single KG. Here we present ConE (Cone Embedding), a KG embedding model that is able to simultaneously model multiple hierarchical as well as non-hierarchical relations in a knowledge graph. ConE embeds entities into hyperbolic cones and models relations as transformations between the cones. In particular, ConE uses cone containment constraints in different subspaces of the hyperbolic embedding space to capture multiple heterogeneous hierarchies. Experiments on standard knowledge graph benchmarks show that ConE obtains state-of-the-art performance on hierarchical reasoning tasks as well as knowledge graph completion task on hierarchical graphs. In particular, our approach yields new state-of-the-art Hits@1 of 45.3% on WN18RR and 16.1% on DDB14 (0.231 MRR). As for hierarchical reasoning task, our approach outperforms previous best results by an average of 20% across the three datasets. 

   more » « less
2. Shadow Cones: A Generalized Framework for Partial Order Embeddings

   Yu, Tao; Liu, Toni; Tseng, Albert; De_Sa, Christopher (May 2024, ICLR 2024)

   Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures. 

   more » « less
3. Directed Scattering for Knowledge Graph-Based Cellular Signaling Analysis

   https://doi.org/10.1109/ICASSP48485.2024.10446530  

   Venkat, Aarthi; Chew, Joyce; Rodriguez, Ferran Cardoso; Tape, Christopher J; Perlmutter, Michael; Krishnaswamy, Smita (April 2024, IEEE)

   Directed graphs are a natural model for many phenomena, in particular scientific knowledge graphs such as molecular interaction or chemical reaction networks that define cellular signaling relationships. In these situations, source nodes typically have distinct biophysical properties from sinks. Due to their ordered and unidirectional relationships, many such networks also have hierarchical and multiscale structure. However, the majority of methods performing node- and edge-level tasks in machine learning do not take these properties into account, and thus have not been leveraged effectively for scientific tasks such as cellular signaling network inference. We propose a new framework called Directed Scattering Autoencoder (DSAE) which uses a directed version of a geometric scattering transform, combined with the non-linear dimensionality reduction properties of an autoencoder and the geometric properties of the hyperbolic space to learn latent hierarchies. We show this method outperforms numerous others on tasks such as embedding directed graphs and learning cellular signaling networks. 

   more » « less
4. Hyperbolic Graph Convolutional Neural Networks

   Chami, I.; Ying, R.; Ré, C.; Leskovec, J. (December 2019, Advances in neural information processing systems)

   Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCNs operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the PubMed dataset. 

   more » « less
5. Representing Hyperbolic Space Accurately using Multi-Component Floats

   Yu Tao; De Sa, Christopher (December 2021, Advances in neural information processing systems)

   Ranzato, M.; Beygelzimer, A.; Dauphin Y.; Liang, P.S.; Wortman Vaughan, J. (Ed.)

   Hyperbolic space is particularly useful for embedding data with hierarchical structure; however, representing hyperbolic space with ordinary floating-point numbers greatly affects the performance due to its \emph{ineluctable} numerical errors. Simply increasing the precision of floats fails to solve the problem and incurs a high computation cost for simulating greater-than-double-precision floats on hardware such as GPUs, which does not support them. In this paper, we propose a simple, feasible-on-GPUs, and easy-to-understand solution for numerically accurate learning on hyperbolic space. We do this with a new approach to represent hyperbolic space using multi-component floating-point (MCF) in the Poincar{\'e} upper-half space model. Theoretically and experimentally we show our model has small numerical error, and on embedding tasks across various datasets, models represented by multi-component floating-points gain more capacity and run significantly faster on GPUs than prior work. 

   more » « less