Related papers: Automated Discovery of New $L$-Function Relations
Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…
Large language models (LLMs) are transforming scientific workflows, not only through their generative capabilities but also through their emerging ability to use tools, reason about data, and coordinate complex analytical tasks. Yet in most…
In recent years L-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs.…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
Analogy is one of the core capacities of human cognition; when faced with new situations, we often transfer prior experience from other domains. Most work on computational analogy relies heavily on complex, manually crafted input. In this…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Recent advancements in the realm of deep learning, particularly in the development of large language models (LLMs), have demonstrated AI's ability to tackle complex mathematical problems or solving programming challenges. However, the…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
Obfuscation poses a persistent challenge for software engineering tasks such as program comprehension, maintenance, testing, and vulnerability detection. While compiler optimizations and third-party code often introduce transformations that…
We study the L-functions associated to Siegel modular forms (equivalently, automorphic representations of ${\rm GSp}(4,\mathbb{A}_{\mathbb{Q}})$) both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform…
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
We introduce a group of related methods for binary classification tasks using probes of the hidden state activations in large language models (LLMs). Performance is on par with the largest and most advanced LLMs currently available, but…
Language identification (LI) is the problem of determining the natural language that a document or part thereof is written in. Automatic LI has been extensively researched for over fifty years. Today, LI is a key part of many text…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
We describe an automated method for identifying classes of morphologically related words in an on-line dictionary, and for linking individual senses in the derived form to one or more senses in the base form by means of morphological…
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…