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Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs)…
We present a hierarchical knowledge graph framework for the structured semantic understanding of visual narratives, using comics as a representative domain for multimodal storytelling. The framework organizes narrative content across three…
Scene graphs are powerful representations that parse images into their abstract semantic elements, i.e., objects and their interactions, which facilitates visual comprehension and explainable reasoning. On the other hand, commonsense…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Natural language definitions of terms can serve as a rich source of knowledge, but structuring them into a comprehensible semantic model is essential to enable them to be used in semantic interpretation tasks. We propose a method and…
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…
We define the notion of sheaf in the context of doctrines. We prove the associate sheaf functor theorem. We show that grothendieck toposes and toposes obtained by the tripos to topos construction are instances of categories of sheaves for a…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
The knowledge-grounded dialogue task aims to generate responses that convey information from given knowledge documents. However, it is a challenge for the current sequence-based model to acquire knowledge from complex documents and…
Foundation models excel at language, where sentences become tokens, and vision, where images become pixels, because both reduce to discrete symbols on a shared, fixed grid. Knowledge Graphs share the discreteness, but not the geometry.…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
In this paper, we propose a novel method for question answering over knowledge graphs based on graph-to-segment mapping, designed to improve the understanding of natural language questions. Our approach is grounded in semantic parsing, a…
We construct Grothendieck topologies on the path category of a finite graph, examining both coarse and discrete cases that offer different perspectives on quiver representations. The coarse topology declares each vertex covered by all…
Research on knowledge graph embeddings has recently evolved into knowledge base embeddings, where the goal is not only to map facts into vector spaces but also constrain the models so that they take into account the relevant conceptual…
We introduce an approach to discovery informatics that uses so called knowledge graphs as the essential representation structure. Knowledge graph is an umbrella term that subsumes various approaches to tractable representation of large…
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…
We define a notion on preadditive categories which plays a role similar to the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive Grothendieck topology and suffices to define…
Knowledge graph embedding, which projects symbolic entities and relations into continuous vector spaces, is gaining increasing attention. Previous methods allow a single static embedding for each entity or relation, ignoring their intrinsic…
The most approaches to Knowledge Base Question Answering are based on semantic parsing. In this paper, we address the problem of learning vector representations for complex semantic parses that consist of multiple entities and relations.…