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Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of…
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such…
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
A not necessarily noetherian local ring O is called regular if every finitely generated ideal I of O possesses finite projective dimension. In the article localizations O of a finitely presented, flat algebra A over a Pruefer domain R at a…
Many natural language processing applications use language models to generate text. These models are typically trained to predict the next word in a sequence, given the previous words and some context such as an image. However, at test time…
We investigate a family of regression problems in a semi-supervised setting. The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points. A goal of semi-supervised learning…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving…
A dichotomy result of Sevenster (2014) completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain "Henkin" or…
Building natural language interfaces typically uses a semantic parser to parse the user's natural language and convert it into structured \textbf{S}emantic \textbf{L}ogic \textbf{F}orms (SLFs). The mainstream approach is to adopt a…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Unsupervised Machine Learning techniques have been applied to Natural Language Processing tasks and surpasses the benchmarks such as GLUE with great success. Building language models approach achieves good results in one language and it can…
Large language models (LLMs) have demonstrated remarkable capabilities across various domains, yet their application to relational deep learning (RDL) remains underexplored. Existing approaches adapt LLMs by traversing relational links…
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…