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Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…
The Smatch metric is a popular method for evaluating graph distances, as is necessary, for instance, to assess the performance of semantic graph parsing systems. However, we observe some issues in the metric that jeopardize meaningful…
Graph plays an important role in representing complex relationships in real-world applications such as social networks, biological data and citation networks. In recent years, Large Language Models (LLMs) have achieved tremendous success in…
Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…
Handwritten Mathematical Expression Recognition is foundational for educational technologies, enabling applications like digital note-taking and automated grading. While modern encoder-decoder architectures with large language models excel…
E-graphs are a data structure that compactly represents equivalent expressions. They are constructed via the repeated application of rewrite rules. Often in practical applications, conditional rewrite rules are crucial, but their…
Graph retrieval-augmented generation (GRAG) places high demands on graph-specific retrievers. However, existing retrievers often rely on language models pretrained on plain text, limiting their effectiveness due to domain misalignment and…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich…
Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal…
This paper presents GRAPHR, the first ReRAM-based graph processing accelerator. GRAPHR follows the principle of near-data processing and explores the opportunity of performing massive parallel analog operations with low hardware and energy…
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…
Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…
Identifying semantically equivalent sentences is important for many cross-lingual and mono-lingual NLP tasks. Current approaches to semantic equivalence take a loose, sentence-level approach to "equivalence," despite previous evidence that…
Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…