Knowledge graph embedding methods are important for the knowledge graph completion (or link prediction) task. One existing efficient method, PairRE, leverages two separate vectors to model complex relations (i.e., 1-to-N, N-to-1, and N-to-N) in knowledge graphs. However, such a method strictly restricts entities on the hyper-ellipsoid surfaces which limits the optimization of entity distribution, leading to suboptimal performance of knowledge graph completion. To address this issue, we propose a novel score function TranSHER, which leverages relation-specific translations between head and tail entities to relax the constraint of hyper-ellipsoid restrictions. By introducing an intuitive and simple relation-specific translation, TranSHER can provide more direct guidance on optimization and capture more semantic characteristics of entities with complex relations. Experimental results show that TranSHER achieves significant performance improvements on link prediction and generalizes well to datasets in different domains and scales. Our codes are public available at https://github.com/yizhilll/TranSHER.
Prior work on integrating text corpora with knowledge graphs (KGs) to improve Knowledge Graph Embedding (KGE) have obtained good performance for entities that co-occur in sentences in text corpora. Such sentences (textual mentions of entity-pairs) are represented as Lexicalised Dependency Paths (LDPs) between two entities. However, it is not possible to represent relations between entities that do not co-occur in a single sentence using LDPs. In this paper, we propose and evaluate several methods to address this problem, where we borrow LDPs from the entity pairs that co-occur in sentences in the corpus (i.e. with mention entity pairs) to represent entity pairs that do not co-occur in any sentence in the corpus (i.e. without mention entity pairs). We propose a supervised borrowing method, SuperBorrow, that learns to score the suitability of an LDP to represent a without-mention entity pair using pre-trained entity embeddings and contextualised LDP representations. Experimental results show that SuperBorrow improves the link prediction performance of multiple widely-used prior KGE methods such as TransE, DistMult, ComplEx and RotatE.
Temporal knowledge graph completion (TKGC) has become a popular approach for reasoning over the event and temporal knowledge graphs, targeting the completion of knowledge with accurate but missing information. In this context, tensor decomposition has successfully modeled interactions between entities and relations. Their effectiveness in static knowledge graph completion motivates us to introduce Time-LowFER, a family of parameter-efficient and time-aware extensions of the low-rank tensor factorization model LowFER. Noting several limitations in current approaches to represent time, we propose a cycle-aware time-encoding scheme for time features, which is model-agnostic and offers a more generalized representation of time. We implement our methods in a unified temporal knowledge graph embedding framework, focusing on time-sensitive data processing. The experiments show that our proposed methods perform on par or better than the state-of-the-art semantic matching models on two benchmarks.
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network analysis methods are applied to the exchange graphs for cluster algebras of varying mutation types. The analysis indicates that when the graphs are represented without identifying by permutation equivalence between clusters an elegant symmetry emerges in the quiver exchange graph embedding. The ratio between number of seeds and number of quivers associated to this symmetry is computed for finite Dynkin type algebras up to rank 5, and conjectured for higher ranks. Simple machine learning techniques successfully learn to classify cluster algebras using the data of seeds. The learning performance exceeds 0.9 accuracies between algebras of the same mutation type and between types, as well as relative to artificially generated data.
Embedding methods have demonstrated robust performance on the task of link prediction in knowledge graphs, by mostly encoding entity relationships. Recent methods propose to enhance the loss function with a literal-aware term. In this paper, we propose KGA: a knowledge graph augmentation method that incorporates literals in an embedding model without modifying its loss function. KGA discretizes quantity and year values into bins, and chains these bins both horizontally, modeling neighboring values, and vertically, modeling multiple levels of granularity. KGA is scalable and can be used as a pre-processing step for any existing knowledge graph embedding model. Experiments on legacy benchmarks and a new large benchmark, DWD, show that augmenting the knowledge graph with quantities and years is beneficial for predicting both entities and numbers, as KGA outperforms the vanilla models and other relevant baselines. Our ablation studies confirm that both quantities and years contribute to KGA's performance, and that its performance depends on the discretization and binning settings. We make the code, models, and the DWD benchmark publicly available to facilitate reproducibility and future research.
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne
Traditionally, theory and practice of Cognitive Control are linked via literature reviews by human domain experts. This approach, however, is inadequate to track the ever-growing literature. It may also be biased, and yield redundancies and confusion. Here we present an alternative approach. We performed automated text analyses on a large body of scientific texts to create a joint representation of tasks and constructs. More specifically, 385,705 scientific abstracts were first mapped into an embedding space using a transformers-based language model. Document embeddings were then used to identify a task-construct graph embedding that grounds constructs on tasks and supports nuanced meaning of the constructs by taking advantage of constrained random walks in the graph. This joint task-construct graph embedding, can be queried to generate task batteries targeting specific constructs, may reveal knowledge gaps in the literature, and inspire new tasks and novel hypotheses.
Knowledge graph embedding (KGE) models represent each entity and relation of a knowledge graph (KG) with low-dimensional embedding vectors. These methods have recently been applied to KG link prediction and question answering over incomplete KGs (KGQA). KGEs typically create an embedding for each entity in the graph, which results in large model sizes on real-world graphs with millions of entities. For downstream tasks these atomic entity representations often need to be integrated into a multi stage pipeline, limiting their utility. We show that an off-the-shelf encoder-decoder Transformer model can serve as a scalable and versatile KGE model obtaining state-of-the-art results for KG link prediction and incomplete KG question answering. We achieve this by posing KG link prediction as a sequence-to-sequence task and exchange the triple scoring approach taken by prior KGE methods with autoregressive decoding. Such a simple but powerful method reduces the model size up to 98% compared to conventional KGE models while keeping inference time tractable. After finetuning this model on the task of KGQA over incomplete KGs, our approach outperforms baselines on multiple large-scale datasets without extensive hyperparameter tuning.
In recent years, we have witnessed the proliferation of knowledge graphs (KG) in various domains, aiming to support applications like question answering, recommendations, etc. A frequent task when integrating knowledge from different KGs is to find which subgraphs refer to the same real-world entity. Recently, embedding methods have been used for entity alignment tasks, that learn a vector-space representation of entities which preserves their similarity in the original KGs. A wide variety of supervised, unsupervised, and semi-supervised methods have been proposed that exploit both factual (attribute based) and structural information (relation based) of entities in the KGs. Still, a quantitative assessment of their strengths and weaknesses in real-world KGs according to different performance metrics and KG characteristics is missing from the literature. In this work, we conduct the first meta-level analysis of popular embedding methods for entity alignment, based on a statistically sound methodology. Our analysis reveals statistically significant correlations of different embedding methods with various meta-features extracted by KGs and rank them in a statistically significant way according to their effectiveness across all real-world KGs of our testbed. Finally, we study interesting trade-offs in terms of methods' effectiveness and efficiency.
Sampled Dense Times Dense Matrix Multiplication (SDDMM) and Sparse Times Dense Matrix Multiplication (SpMM) appear in diverse settings, such as collaborative filtering, document clustering, and graph embedding. Frequently, the SDDMM output becomes the input sparse matrix for a subsequent SpMM operation. Existing work has focused on shared memory parallelization of these primitives. While there has been extensive analysis of communication-minimizing distributed 1.5D algorithms for SpMM, no such analysis exists for SDDMM or the back-to-back sequence of SDDMM and SpMM, termed FusedMM. We show that distributed memory 1.5D and 2.5D algorithms for SpMM can be converted to algorithms for SDDMM with identical communication costs and input / output data layouts. Further, we give two communication-eliding strategies to reduce costs further for FusedMM kernels: either reusing the replication of an input dense matrix for the SDDMM and SpMM in sequence, or fusing the local SDDMM and SpMM kernels. We benchmark FusedMM algorithms on Cori, a Cray XC40 at LBNL, using Erdos-Renyi random matrices and large real-world sparse matrices. On 256 nodes with 68 cores each, 1.5D FusedMM algorithms using either communication eliding approach can save at least 30% of time spent exclusively in communication compared to executing a distributed-memory SpMM and SDDMM kernel in sequence. On real-world matrices with hundreds of millions of edges, all of our algorithms exhibit at least a 10x speedup over the SpMM algorithm in PETSc. On these matrices, our communication-eliding techniques exhibit runtimes up to 1.6 times faster than an unoptimized sequence of SDDMM and SpMM. We embed and test the scaling of our algorithms in real-world applications, including collaborative filtering via alternating-least-squares and inference for attention-based graph neural networks.
The link prediction task on knowledge graphs without explicit negative triples in the training data motivates the usage of rank-based metrics. Here, we review existing rank-based metrics and propose desiderata for improved metrics to address lack of interpretability and comparability of existing metrics to datasets of different sizes and properties. We introduce a simple theoretical framework for rank-based metrics upon which we investigate two avenues for improvements to existing metrics via alternative aggregation functions and concepts from probability theory. We finally propose several new rank-based metrics that are more easily interpreted and compared accompanied by a demonstration of their usage in a benchmarking of knowledge graph embedding models.
Knowledge graph completion (KGC) aims to reason over known facts and infer the missing links. Text-based methods such as KGBERT (Yao et al., 2019) learn entity representations from natural language descriptions, and have the potential for inductive KGC. However, the performance of text-based methods still largely lag behind graph embedding-based methods like TransE (Bordes et al., 2013) and RotatE (Sun et al., 2019b). In this paper, we identify that the key issue is efficient contrastive learning. To improve the learning efficiency, we introduce three types of negatives: in-batch negatives, pre-batch negatives, and self-negatives which act as a simple form of hard negatives. Combined with InfoNCE loss, our proposed model SimKGC can substantially outperform embedding-based methods on several benchmark datasets. In terms of mean reciprocal rank (MRR), we advance the state-of-the-art by +19% on WN18RR, +6.8% on the Wikidata5M transductive setting, and +22% on the Wikidata5M inductive setting. Thorough analyses are conducted to gain insights into each component. Our code is available at https://github.com/intfloat/SimKGC .
Unsupervised graph representation learning aims to distill various graph information into a downstream task-agnostic dense vector embedding. However, existing graph representation learning approaches are designed mainly under the node homophily assumption: connected nodes tend to have similar labels and optimize performance on node-centric downstream tasks. Their design is apparently against the task-agnostic principle and generally suffers poor performance in tasks, e.g., edge classification, that demands feature signals beyond the node-view and homophily assumption. To condense different feature signals into the embeddings, this paper proposes PairE, a novel unsupervised graph embedding method using two paired nodes as the basic unit of embedding to retain the high-frequency signals between nodes to support node-related and edge-related tasks. Accordingly, a multi-self-supervised autoencoder is designed to fulfill two pretext tasks: one retains the high-frequency signal better, and another enhances the representation of commonality. Our extensive experiments on a diversity of benchmark datasets clearly show that PairE outperforms the unsupervised state-of-the-art baselines, with up to 101.1\% relative improvement on the edge classification tasks that rely on both the high and low-frequency signals in the pair and up to 82.5\% relative performance gain on the node classification tasks.
Knowledge graphs store a large number of factual triples while they are still incomplete, inevitably. The previous knowledge graph completion (KGC) models predict missing links between entities merely relying on fact-view data, ignoring the valuable commonsense knowledge. The previous knowledge graph embedding (KGE) techniques suffer from invalid negative sampling and the uncertainty of fact-view link prediction, limiting KGC's performance. To address the above challenges, we propose a novel and scalable Commonsense-Aware Knowledge Embedding (CAKE) framework to automatically extract commonsense from factual triples with entity concepts. The generated commonsense augments effective self-supervision to facilitate both high-quality negative sampling (NS) and joint commonsense and fact-view link prediction. Experimental results on the KGC task demonstrate that assembling our framework could enhance the performance of the original KGE models, and the proposed commonsense-aware NS module is superior to other NS techniques. Besides, our proposed framework could be easily adaptive to various KGE models and explain the predicted results.
NeuralKG is an open-source Python-based library for diverse representation learning of knowledge graphs. It implements three different series of Knowledge Graph Embedding (KGE) methods, including conventional KGEs, GNN-based KGEs, and Rule-based KGEs. With a unified framework, NeuralKG successfully reproduces link prediction results of these methods on benchmarks, freeing users from the laborious task of reimplementing them, especially for some methods originally written in non-python programming languages. Besides, NeuralKG is highly configurable and extensible. It provides various decoupled modules that can be mixed and adapted to each other. Thus with NeuralKG, developers and researchers can quickly implement their own designed models and obtain the optimal training methods to achieve the best performance efficiently. We built an website in http://neuralkg.zjukg.cn to organize an open and shared KG representation learning community. The source code is all publicly released at https://github.com/zjukg/NeuralKG.
Relation context has been proved to be useful for many challenging vision tasks. In the field of 3D object detection, previous methods have been taking the advantage of context encoding, graph embedding, or explicit relation reasoning to extract relation context. However, there exists inevitably redundant relation context due to noisy or low-quality proposals. In fact, invalid relation context usually indicates underlying scene misunderstanding and ambiguity, which may, on the contrary, reduce the performance in complex scenes. Inspired by recent attention mechanism like Transformer, we propose a novel 3D attention-based relation module (ARM3D). It encompasses object-aware relation reasoning to extract pair-wise relation contexts among qualified proposals and an attention module to distribute attention weights towards different relation contexts. In this way, ARM3D can take full advantage of the useful relation context and filter those less relevant or even confusing contexts, which mitigates the ambiguity in detection. We have evaluated the effectiveness of ARM3D by plugging it into several state-of-the-art 3D object detectors and showing more accurate and robust detection results. Extensive experiments show the capability and generalization of ARM3D on 3D object detection. Our source code is available at https://github.com/lanlan96/ARM3D.
The effectiveness of knowledge graph embedding (KGE) largely depends on the ability to model intrinsic relation patterns and mapping properties. However, existing approaches can only capture some of them with insufficient modeling capacity. In this work, we propose a more powerful KGE framework named HousE, which involves a novel parameterization based on two kinds of Householder transformations: (1) Householder rotations to achieve superior capacity of modeling relation patterns; (2) Householder projections to handle sophisticated relation mapping properties. Theoretically, HousE is capable of modeling crucial relation patterns and mapping properties simultaneously. Besides, HousE is a generalization of existing rotation-based models while extending the rotations to high-dimensional spaces. Empirically, HousE achieves new state-of-the-art performance on five benchmark datasets. Our code is available at https://github.com/anrep/HousE.
Graph convolutional networks (GCNs) -- which are effective in modeling graph structures -- have been increasingly popular in knowledge graph completion (KGC). GCN-based KGC models first use GCNs to generate expressive entity representations and then use knowledge graph embedding (KGE) models to capture the interactions among entities and relations. However, many GCN-based KGC models fail to outperform state-of-the-art KGE models though introducing additional computational complexity. This phenomenon motivates us to explore the real effect of GCNs in KGC. Therefore, in this paper, we build upon representative GCN-based KGC models and introduce variants to find which factor of GCNs is critical in KGC. Surprisingly, we observe from experiments that the graph structure modeling in GCNs does not have a significant impact on the performance of KGC models, which is in contrast to the common belief. Instead, the transformations for entity representations are responsible for the performance improvements. Based on the observation, we propose a simple yet effective framework named LTE-KGE, which equips existing KGE models with linearly transformed entity embeddings. Experiments demonstrate that LTE-KGE models lead to similar performance improvements with GCN-based KGC methods, while being more computationally efficient. These results suggest that existing GCNs are unnecessary for KGC, and novel GCN-based KGC models should count on more ablation studies to validate their effectiveness. The code of all the experiments is available on GitHub at https://github.com/MIRALab-USTC/GCN4KGC.
The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.
Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.