Related papers: Coding-Logic Correspondence: Turning Information a…

The finite set of subsystems of a finite quantum system with variables in ${\mathbb Z}(n)$, is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more…

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of…

Given unstructured text, Large Language Models (LLMs) are adept at answering simple (single-hop) questions. However, as the complexity of the questions increase, the performance of LLMs degrade. We believe this is due to the overhead…

Knowledge graphs are an expressive and widely used data structure due to their ability to integrate data from different domains in a sensible and machine-readable way. Thus, they can be used to model a variety of systems such as molecules…

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple…

We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…

Despite the superb performance in many tasks, large language models (LLMs) bear the risk of generating hallucination or even wrong answers when confronted with tasks that demand the accuracy of knowledge. The issue becomes even more…

This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…

Machine reading comprehension (MRC) poses new challenges over logical reasoning, which aims to understand the implicit logical relations entailed in the given contexts and perform inference over them. Due to the complexity of logic, logical…

Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…

Gradient coding allows a master node to derive the aggregate of the partial gradients, calculated by some worker nodes over the local data sets, with minimum communication cost, and in the presence of stragglers. In this paper, for gradient…

We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory.…

Federated learning can enable remote workers to collaboratively train a shared machine learning model while allowing training data to be kept locally. In the use case of wireless mobile devices, the communication overhead is a critical…

In the real-world question answering scenarios, hybrid form combining both tabular and textual contents has attracted more and more attention, among which numerical reasoning problem is one of the most typical and challenging problems.…

Despite the advances in large language models (LLMs), how they use their knowledge for reasoning is not yet well understood. In this study, we propose a method that deconstructs complex real-world questions into a graph, representing each…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

We consider a problem of coding for computing, where the decoder wishes to estimate a function of its local message and the source message at the encoder within a given distortion. We show that the rate-distortion function can be…