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In this note we characterize, within the framework of the theory of finite set, those categories of graphs that are {\em algebraic universal} in the sense that every concrete category embeds in them. The proof of the characterization is…
Foundation models like ChatGPT and GPT-4 have revolutionized artificial intelligence, exhibiting remarkable abilities to generalize across a wide array of tasks and applications beyond their initial training objectives. However, graph…
Accurate syntactic representations are essential for robust generalization in natural language. Recent work has found that pre-training can teach language models to rely on hierarchical syntactic features - as opposed to incorrect linear…
Automated short answer grading (ASAG) is critical for scaling educational assessment, yet large language models (LLMs) often struggle with hallucinations and strict rubric adherence due to their reliance on generalized pre-training. While…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
Typed metagraphs are defined as hypergraphs with types assigned to hyperedges and their targets, and the potential to have targets of hyperedges connect to whole links as well as targets. Directed typed metagraphs (DTMGs) are introduced via…
Most existing text generation models follow the sequence-to-sequence paradigm. Generative Grammar suggests that humans generate natural language texts by learning language grammar. We propose a syntax-guided generation schema, which…
Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many…
Semantic segmentation models are typically trained on a fixed set of classes, limiting their applicability in open-world scenarios. Class-incremental semantic segmentation aims to update models with emerging new classes while preventing…
Graph Anomaly Detection (GAD) aims to identify atypical graph entities, such as nodes, edges, or substructures, that deviate significantly from the majority. While existing text-rich approaches typically integrate structural context into…
Formalizing cooking procedures remains a challenging task due to their inherent complexity and ambiguity. We introduce an extensible domain-specific language for representing recipes as directed action graphs, capturing processes,…
The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…
Modern generative pre-trained language models excel at open-ended text generation, yet continue to underperform on structure-related tasks such as NER, relation extraction, and semantic role labeling, especially when compared to…
This paper describes a new kind of knowledge representation and mining system which we are calling the Semantic Knowledge Graph. At its heart, the Semantic Knowledge Graph leverages an inverted index, along with a complementary uninverted…
Supertagging is an approach originally developed by Bangalore and Joshi (1999) to improve the parsing efficiency. In the beginning, the scholars used small training datasets and somewhat na\"ive smoothing techniques to learn the probability…
Knowledge graphs can represent information about the real-world using entities and their relations in a structured and semantically rich manner and they enable a variety of downstream applications such as question-answering, recommendation…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
We develop a shape analysis for reasoning about relational properties of data structures. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is parameterized by user-supplied indexed graph grammars to…
Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…