Related papers: Coding-Logic Correspondence: Turning Information a…
Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…
A network-theoretic approach for determining the complexity of a graph is proposed. This approach is based on the relationship between the linear algebra (theory of determinants) and the graph theory. In this paper we contribute a new…
The movement of data (communication) between levels of a memory hierarchy, or between parallel processors on a network, can greatly dominate the cost of computation, so algorithms that minimize communication are of interest. Motivated by…
This paper presents our novel method to encode word confusion networks, which can represent a rich hypothesis space of automatic speech recognition systems, via recurrent neural networks. We demonstrate the utility of our approach for the…
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…
In this paper hypergraph Lambek calculus ($\mathrm{HL}$) is presented. This formalism aims to generalize the Lambek calculus ($\mathrm{L}$) to hypergraphs as hyperedge replacement grammars extend context-free grammars. In contrast to the…
We continue to develop a research line initiated in \cite{wollic22}, studying I/O logic from an algebraic approach based on subordination algebras. We introduce the classes of slanted (co-)Heyting algebras as equivalent presentations of…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
Reasoning is a fundamental problem for computers and deeply studied in Artificial Intelligence. In this paper, we specifically focus on answering multi-hop logical queries on Knowledge Graphs (KGs). This is a complicated task because, in…
In the realm of Large Language Model (LLM) inference, the inherent structure of transformer models coupled with the multi-GPU tensor parallelism strategy leads to a sequential execution of computation and communication. This results in…
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…
Large language models (LLMs) have recently achieved remarkable success in various reasoning tasks in the field of natural language processing. This success of LLMs has also motivated their use in graph-related tasks. Among others, recent…
By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which…
We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
As a pivotal task in data lake management, joinable table discovery has attracted widespread interest. While existing language model-based methods achieve remarkable performance by combining offline column representation learning with…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the…
Semantic communication is envisioned as a promising technique to break through the Shannon limit. However, the existing semantic communication frameworks do not involve inference and error correction, which limits the achievable…
Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…