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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. 

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2. Nomenclature over 5 years in TaxonWorks: Approach, implementation, limitations and outcomes

   https://doi.org/10.3897/biss.5.75441  

   Yoder, Matthew ; Dmitriev, Dmitry ( September 2021 , Biodiversity Information Science and Standards)

   We are now over four decades into digitally managing the names of Earth's species. As the number of federating (i.e., software that brings together previously disparate projects under a common infrastructure, for example TaxonWorks) and aggregating (e.g., International Plant Name Index, Catalog of Life (CoL)) efforts increase, there remains an unmet need for both the migration forward of old data, and for the production of new, precise and comprehensive nomenclatural catalogs. Given this context, we provide an overview of how TaxonWorks seeks to contribute to this effort, and where it might evolve in the future. In TaxonWorks, when we talk about governed names and relationships, we mean it in the sense of existing international codes of nomenclature (e.g., the International Code of Zoological Nomenclature (ICZN)). More technically, nomenclature is defined as a set of objective assertions that describe the relationships between the names given to biological taxa and the rules that determine how those names are governed. It is critical to note that this is not the same thing as the relationship between a name and a biological entity, but rather nomenclature in TaxonWorks represents the details of the (governed) relationships between names. Rather than thinking of nomenclature as changing (a verb commonly used to express frustration with biological nomenclature), it is useful to think of nomenclature as a set of data points, which grows over time. For example, when synonymy happens, we do not erase the past, but rather record a new context for the name(s) in question. The biological concept changes, but the nomenclature (names) simply keeps adding up. Behind the scenes, nomenclature in TaxonWorks is represented by a set of nodes and edges, i.e., a mathematical graph, or network (e.g., Fig. 1). Most names (i.e., nodes in the network) are what TaxonWorks calls "protonyms," monomial epithets that are used to construct, for example, bionomial names (not to be confused with "protonym" sensu the ICZN). Protonyms are linked to other protonyms via relationships defined in NOMEN, an ontology that encodes governed rules of nomenclature. Within the system, all data, nodes and edges, can be cited, i.e., linked to a source and therefore anchored in time and tied to authorship, and annotated with a variety of annotation types (e.g., notes, confidence levels, tags). The actual building of the graphs is greatly simplified by multiple user-interfaces that allow scientists to review (e.g. Fig. 2), create, filter, and add to (again, not "change") the nomenclatural history. As in any complex knowledge-representation model, there are outlying scenarios, or edge cases that emerge, making certain human tasks more complex than others. TaxonWorks is no exception, it has limitations in terms of what and how some things can be represented. While many complex representations are hidden by simplified user-interfaces, some, for example, the handling of the ICZN's Family-group name, batch-loading of invalid relationships, and comparative syncing against external resources need more work to simplify the processes presently required to meet catalogers' needs. The depth at which TaxonWorks can capture nomenclature is only really valuable if it can be used by others. This is facilitated by the application programming interface (API) serving its data (https://api.taxonworks.org), serving text files, and by exports to standards like the emerging Catalog of Life Data Package. With reference to real-world problems, we illustrate different ways in which the API can be used, for example, as integrated into spreadsheets, through the use of command line scripts, and serve in the generation of public-facing websites. Behind all this effort are an increasing number of people recording help videos, developing documentation, and troubleshooting software and technical issues. Major contributions have come from developers at many skill levels, from high school to senior software engineers, illustrating that TaxonWorks leads in enabling both technical and domain-based contributions. The health and growth of this community is a key factor in TaxonWork's potential long-term impact in the effort to unify the names of Earth's species. 

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3. Spatio-Temporal Event Forecasting Using Incremental Multi-Source Feature Learning

   https://doi.org/10.1145/3464976  

   Zhao, Liang ; Gao, Yuyang ; Ye, Jieping ; Chen, Feng ; Ye, Yanfang ; Lu, Chang-Tien ; Ramakrishnan, Naren ( April 2022 , ACM Transactions on Knowledge Discovery from Data)

   The forecasting of significant societal events such as civil unrest and economic crisis is an interesting and challenging problem which requires both timeliness, precision, and comprehensiveness. Significant societal events are influenced and indicated jointly by multiple aspects of a society, including its economics, politics, and culture. Traditional forecasting methods based on a single data source find it hard to cover all these aspects comprehensively, thus limiting model performance. Multi-source event forecasting has proven promising but still suffers from several challenges, including (1) geographical hierarchies in multi-source data features, (2) hierarchical missing values, (3) characterization of structured feature sparsity, and (4) difficulty in model’s online update with incomplete multiple sources. This article proposes a novel feature learning model that concurrently addresses all the above challenges. Specifically, given multi-source data from different geographical levels, we design a new forecasting model by characterizing the lower-level features’ dependence on higher-level features. To handle the correlations amidst structured feature sets and deal with missing values among the coupled features, we propose a novel feature learning model based on an N th-order strong hierarchy and fused-overlapping group Lasso. An efficient algorithm is developed to optimize model parameters and ensure global optima. More importantly, to enable the model update in real time, the online learning algorithm is formulated and active set techniques are leveraged to resolve the crucial challenge when new patterns of missing features appear in real time. Extensive experiments on 10 datasets in different domains demonstrate the effectiveness and efficiency of the proposed models. 

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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. 

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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. 

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