相关论文: Implementing Tensor Logic: Unifying Datalog and Ne…

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…

The unification of low-level perception and high-level reasoning is a long-standing problem in artificial intelligence, which has the potential to not only bring the areas of logic and learning closer together but also demonstrate how…

We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable…

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…

We introduce a new logic programming language T-PRISM based on tensor embeddings. Our embedding scheme is a modification of the distribution semantics in PRISM, one of the state-of-the-art probabilistic logic programming languages, by…

Knowledge graph embedding models have gained significant attention in AI research. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine…

The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified…

Large language models (LLMs) have achieved impressive human-like performance across various reasoning tasks. However, their mastery of underlying inferential rules still falls short of human capabilities. To investigate this, we propose a…

A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define…

We provide a comparative study between neural word representations and traditional vector spaces based on co-occurrence counts, in a number of compositional tasks. We use three different semantic spaces and implement seven tensor-based…

Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…

We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…

Social norms underlie all human social interactions, yet formalizing and reasoning with them remains a major challenge for AI systems. We present a novel system for taking social rules of thumb (ROTs) in natural language from the Social…

Answering compositional questions that require multiple steps of reasoning against text is challenging, especially when they involve discrete, symbolic operations. Neural module networks (NMNs) learn to parse such questions as executable…