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. 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. In numerous practical situations, graphs exhibit temporal characteristics, as seen in applications like social networks, citation graphs, and bank transactions, among others (Kazemi et al., 2020). These temporal graphs can be divided into two types: 1) temporal graphs with constant graph structure (Grassi et al., 2017; Cao et al., 2020), and 2) temporal graphs with dynamic structures (Zhou et al., 2022; Bastos et al., 2023; da Xu et al., 2020). Our focus in this work is the latter case. The evolving graphs have been comprehensively studied from the spatio-temporal graph-neural network (GNN) perspective, focusing on propagating local information (Pareja et al., 2020; Shi et al., 2021; Xiang et al., 2022; da Xu et al., 2020). Albeit the success of spectral GNNs for static graphs for capturing non-local dependencies in graph signals (Wang & Zhang, 2022), they have not been applied to temporal graphs with evolving structure. To make spectral GNN work for temporal graphs effectively and efficiently, there is a necessity for an invertible transform that collectively captures evolving spectra along the graph vertex and time domain.

In this paper we present a novel method, $\textit{Knowledge Persistence}$ ($\mathcal{KP}$), 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. $\mathcal{KP}$ 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 $\mathcal{KP}$ 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 $\mathcal{KP}$ 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 $\mathcal{KP}$), and on average (across methods & data) reduces the evaluation time (validation+test) by $\approx$ $\textbf{99.96}\%$.

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 a novel 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.

We present a novel method for relation extraction (RE) from a single sentence, mapping the sentence and two given entities to a canonical fact in a knowledge graph (KG). Especially in this presumed sentential RE setting, the context of a single sentence is often sparse. This paper introduces the KGPool method to address this sparsity, dynamically expanding the context with additional facts from the KG. It learns the representation of these facts (entity alias, entity descriptions, etc.) using neural methods, supplementing the sentential context. Unlike existing methods that statically use all expanded facts, KGPool conditions this expansion on the sentence. We study the efficacy of KGPool by evaluating it with different neural models and KGs (Wikidata and NYT Freebase). Our experimental evaluation on standard datasets shows that by feeding the KGPool representation into a Graph Neural Network, the overall method is significantly more accurate than state-of-the-art methods.

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. RECON reports 87.23 F1 score (Vs 82.29 baseline) on Wikidata dataset whereas on NYT Freebase, reported values are 87.5(P@10) and 74.1(P@30) compared to the previous baseline scores of 81.3(P@10) and 63.1(P@30).