We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with \eft for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation, which essentially only captures the low pass signals and local interactions. In this work, we go beyond current approaches to incorporate global features for effectively learning representations of a dynamically evolving graph. We propose to do so by capturing the spectrum of the dynamic graph. Since static methods to learn the graph spectrum would not consider the history of the evolution of the spectrum as the graph evolves with time, we propose an approach to learn the graph wavelets to capture this evolving spectra. Further, we propose a framework that integrates the dynamically captured spectra in the form of these learnable wavelets into spatial features for incorporating local and global interactions. Experiments on eight standard datasets show that our method significantly outperforms related methods on various tasks for dynamic graphs.

In this paper we present a novel method, Knowledge Persistence (), for faster evaluation of Knowledge Graph (KG) completion approaches. Current ranking-based evaluation is quadratic in the size of the KG, leading to long evaluation times and consequently a high carbon footprint. addresses this by representing the topology of the KG completion methods through the lens of topological data analysis, concretely using persistent homology. The characteristics of persistent homology allow to evaluate the quality of the KG completion looking only at a fraction of the data. Experimental results on standard datasets show that the proposed metric is highly correlated with ranking metrics (Hits@N, MR, MRR). Performance evaluation shows that is computationally efficient: In some cases, the evaluation time (validation+test) of a KG completion method has been reduced from 18 hours (using Hits@10) to 27 seconds (using ), and on average (across methods & data) reduces the evaluation time (validation+test) by ≈ 99.96%.

Recently, several Knowledge Graph Embedding (KGE) approaches have been devised to represent entities and relations in a dense vector space and employed in downstream tasks such as link prediction. A few KGE techniques address interpretability, i.e., mapping the connectivity patterns of the relations (symmetric/asymmetric, inverse, and composition) to a geometric interpretation such as rotation. Other approaches model the representations in higher dimensional space such as four-dimensional space (4D) to enhance the ability to infer the connectivity patterns (i.e., expressiveness). However, modeling relation and entity in a 4D space often comes at the cost of interpretability. We propose HopfE, a novel KGE approach aiming to achieve the interpretability of inferred relations in the four-dimensional space. HopfE models the structural embeddings in 3D Euclidean space. Next, we map the entity embedding vector from a 3D Euclidean space to a 4D hypersphere using the inverse Hopf Fibration, in which we embed the semantic information from the KG ontology. Thus, HopfE considers the structural and semantic properties of the entities without losing expressivity and interpretability. Our empirical results on four well-known benchmarks achieve state-of-the-art performance for KG completion.

In this paper, we present a novel method named RECON, that automatically identifies relations in a sentence (sentential relation extraction) and aligns to a knowledge graph (KG). RECON uses a graph neural network to learn representations of both the sentence as well as facts stored in a KG, improving the overall extraction quality. These facts, including entity attributes (label, alias, description, instance-of) and factual triples, have not been collectively used in the state of the art methods. We evaluate the effect of various forms of representing the KG context on the performance of RECON. The empirical evaluation on two standard relation extraction datasets shows that RECON significantly outperforms all state of the art methods on NYT Freebase and Wikidata datasets.

Pretrained Transformer models have emerged as state-of-the-art approaches that learn contextual information from the text to improve the performance of several NLP tasks. These models, albeit powerful, still require specialized knowledge in specific scenarios. In this paper, we argue that context derived from a knowledge graph (in our case: Wikidata) provides enough signals to inform pretrained transformer models and improve their performance for named entity disambiguation (NED) on Wikidata KG. We further hypothesize that our proposed KG context can be standardized for Wikipedia, and we evaluate the impact of KG context on the state of the art NED model for the Wikipedia knowledge base. Our empirical results validate that the proposed KG context can be generalized (for Wikipedia), and providing KG context in transformer architectures considerably outperforms the existing baselines, including the vanilla transformer models.