Related papers: The Network Structure of Mathlib
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Complex networks are relational data sets commonly represented as graphs. The analysis of their intricate structure is relevant to many areas of science and commerce, and data sets may reach sizes that require distributed storage and…
CSLib is an emerging Lean 4 library for computer-science formalization, but its premise-retrieval behavior is not well represented by broad mathematical theorem-proving benchmarks. We introduce CSLibPremiseBench, a reproducible…
Large language models (LLMs) leverage deep learning architectures to process and predict sequences of words, enabling them to perform a wide range of natural language processing tasks, such as translation, summarization, question answering,…
We introduce LinAlg-Bench, a diagnostic benchmark evaluating 10 frontier large language models on structured linear algebra computation across a strict dimensional gradient of 3x3, 4x4, and 5x5 matrices. Spanning 9 task types and 660…
Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature,…
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We explain how a coherent logarithmic scheme $X$ has a natural…
Large language models have been extensively studied as neural knowledge bases for their knowledge access, editability, reasoning, and explainability. However, few works focus on the structural patterns of their knowledge. Motivated by this…
Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…
Graph-structured data underpins applications from citation analysis and social-network modeling to molecular design and knowledge-graph construction, and Large Language Models (LLMs) are increasingly used as prompt-driven graph…
Reliable autoformalization remains challenging even in the era of large language models (LLMs). The scarcity of high-quality training data is a major bottleneck. Expert annotation requires substantial time and deep expertise in both…
Recent years have witnessed the success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
It is evident that the current state of Large Language Models (LLMs) necessitates the incorporation of external tools. The lack of straightforward algebraic and logical reasoning is well documented and prompted researchers to develop…
The ecosystem of Lean and Mathlib has become the de facto standard for large language model (LLM) assisted formal reasoning with remarkable successes in recent years. Those successes, however, only consume Mathlib as an essential dependency…