Related papers: The Network Structure of Mathlib

Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

In this article, we describe the architecture of the LIMA (Libre Multilingual Analyzer) framework and its recent evolution with the addition of new text analysis modules based on deep neural networks. We extended the functionality of LIMA…

Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…

Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…

Recent research has highlighted the role of relational inductive biases in building learning agents that can generalize and reason in a compositional manner. However, while relational learning algorithms such as graph neural networks (GNNs)…

Large language models (LLMs) solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. To understand this gap, we synthesize cognitive…

Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to more complex problems. This is difficult to study, as (i) much of the available evaluation data has…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

In the 20th century, newly invented technical artifacts were connected to form large-scale complex engineering systems. Furthermore, the interactions found within these networked systems has grown in both degree as well as heterogeneity.…

Computational paths treat propositional equality as explicit paths built from labelled deduction steps and rewrite rules. This view originates in work by de Queiroz and collaborators [1] and yields a weak groupoid structure for equality,…

A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…

Binary vulnerability analysis is increasingly performed by LLM-based agents in an iterative, multi-pass manner, with the model as the core decision-maker. However, how such systems organize exploration over hundreds of reasoning steps…

Large Language Models (LLMs), excel in natural language understanding, but their capability for complex mathematical reasoning with an amalgamation of structured tables and unstructured text is uncertain. This study explores LLMs'…

While achieving remarkable progress in a broad range of tasks, large language models (LLMs) remain significantly limited in properly using massive external tools. Existing in-context learning approaches simply format tools into a list of…

Large language models (LLMs) can support scientific literature synthesis, but remain prone to hallucinated references, uneven coverage, and weakly grounded thematic organization. We evaluate whether bibliometric structure improves…

An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…

As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

Large language models often generate homogeneous outputs, but whether this is problematic depends on the specific task. For objective math tasks, responses may vary in terms of problem-solving strategy but should maintain the same…