Related papers: Automated Discovery of New $L$-Function Relations
In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered…
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept…
Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most…
Automated theorem proving is essential for the formal verification of safety-critical systems. As the corpus of formal proofs grows, a natural paradigm is to learn from existing proofs. However, current learning-based approaches…
Feature transformation enhances data representation by deriving new features from the original data. Generative AI offers potential for this task, but faces challenges in stable generation (consistent outputs) and valid generation…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use…
In this work we present work in progress on functionality duplication detection in logic programs. Eliminating duplicated functionality recently became prominent in context of refactoring. We describe a quantitative approach that allows to…
Today with Big Data and data lakes, we are faced of a mass of data that is very difficult to manage it manually. The protection of personal data in this context requires an automatic analysis for data discovery. Storing the names of…
Large Language Models (LLMs) are transforming scientific hypothesis generation and validation by enabling information synthesis, latent relationship discovery, and reasoning augmentation. This survey provides a structured overview of…
Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…
Big Data analytics and Artificial Intelligence systems derive non-intuitive and often unverifiable inferences about individuals' behaviors, preferences, and private lives. Drawing on diverse, feature-rich datasets of unpredictable value,…
We claim that LLMs can be paired with formal analysis methods to provide accessible, relevant feedback for HRI tasks. While logic specifications are useful for defining and assessing a task, these representations are not easily interpreted…
We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae,…
Automated Machine Learning (AutoML) technology can lower barriers in data work yet still requires human intervention to be functional. However, the complex and collaborative process resulting from humans and machines trading off work makes…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
This work has been motivated by two long term goals: to understand how humans learn language and to build programs that can understand language. Using a representation that makes the relevant features explicit is a prerequisite for…