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Although deep neural networks have demonstrated significant success due to their powerful expressiveness, most models struggle to meet practical requirements for uncertainty estimation. Concurrently, the entangled nature of deep neural…
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
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…
Multilayer networks describe the rich ways in which nodes are related by accounting for different relationships in separate layers. These multiple relationships are naturally represented by an adjacency tensor. In this work we study the use…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
Large Language Models appear competent when answering general questions but often fail when pushed into domain-specific details. No existing methodology provides an out-of-the-box solution for measuring how deeply LLMs can sustain accurate…
Knowledge-Enhanced Pre-trained Language Models (KEPLMs) are pre-trained models with relation triples injecting from knowledge graphs to improve language understanding abilities. To guarantee effective knowledge injection, previous studies…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Learning disentangled representations of natural language is essential for many NLP tasks, e.g., conditional text generation, style transfer, personalized dialogue systems, etc. Similar problems have been studied extensively for other forms…
Knowledge Graphs are pivotal for semantic data integration. The real-world data they model is often inherently uncertain. Within knowledge graphs, uncertainty manifests in three distinct levels: imprecise attribute values, probabilistic…
With the rapid growth of e-commerce, exploring general representations rather than task-specific ones has attracted increasing attention. Although recent multimodal large language models (MLLMs) have driven significant progress in product…
Recent language models enable new opportunities for structured reasoning with text, such as the construction of intuitive, proof-like textual entailment trees without relying on brittle formal logic. However, progress in this direction has…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
Ontology embeddings map classes, roles, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
Grounding responses in external knowledge represents an effective strategy for mitigating hallucinations in Large Language Models (LLMs). However, current LLMs struggle to seamlessly integrate knowledge while simultaneously maintaining…
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…
Various models have been proposed to incorporate knowledge of syntactic structures into neural language models. However, previous works have relied heavily on elaborate components for a specific language model, usually recurrent neural…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We introduce C3LLM (Conditioned-on-Three-Modalities Large Language Models), a novel framework combining three tasks of video-to-audio, audio-to-text, and text-to-audio together. C3LLM adapts the Large Language Model (LLM) structure as a…
Although large language models (LLMs) excel in knowledge recall and reasoning, their static nature leads to outdated information as the real world evolves or when adapting to domain-specific knowledge, highlighting the need for effective…