Related papers: Learning Algebraic Structures: Preliminary Investi…
While a real-world research program in mathematics may be guided by a motivating question, the process of mathematical discovery is typically open-ended. Ideally, exploration needed to answer the original question will reveal new…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3…
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…
In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power…
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…
Discovering discrete algebraic rules from data is a fundamental challenge in machine learning. We formalize this problem through Cayley-table completion -- an algebraic counterpart to classical matrix completion -- where the degree of…
The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the…
We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the class $\mathbf{InfEx}_{\cong}$, consisting of the…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…
Many modern machine learning approaches require vast amounts of training data to learn new concepts; conversely, human learning often requires few examples--sometimes only one--from which the learner can abstract structural concepts. We…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…