相关论文: The Ramanujan Library -- Automated Discovery on th…
A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
Document subject classification is essential for structuring (digital) libraries and allowing readers to search within a specific field. Currently, the classification is typically made by human domain experts. Semi-supervised Machine…
Mathematical formulas serve as the means of communication between humans and nature, encapsulating the operational laws governing natural phenomena. The concise formulation of these laws is a crucial objective in scientific research and an…
High-volume feature-rich data sets are becoming the bread-and-butter of 21st century astronomy but present significant challenges to scientific discovery. In particular, identifying scientifically significant relationships between sets of…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
D. Bailey and R. E. Crandall recently formulated a "Hypothesis A", which provides a general principle to explain the (conjectured) normality of constants like pi or log 2 and other related numbers, to base 2 or other integer bases. This…
Real-world information needs require access to structurally diverse knowledge sources, from unstructured text and relational tables to knowledge graphs and property graphs. Existing retrievers, however, operate over one source at a time…
We present a constant-round algorithm in the massively parallel computation (MPC) model for evaluating a natural join where every input relation has two attributes. Our algorithm achieves a load of $\tilde{O}(m/p^{1/\rho})$ where $m$ is the…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, joint interactions of proteins, to name a few. In this work, we propose tools for answering the…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Reinforcement learning (RL) has proven itself as a powerful tool for the discovery of quantum circuits and quantum protocols. We have recently shown that including composite quantum gates -- referred to as ``gadgets'' -- in the action space…
Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of…
Large Language Models (LLMs) have emerged as powerful tools for accelerating scientific discovery, yet their static knowledge and hallucination issues hinder autonomous research applications. Recent advances integrate LLMs into agentic…
Retrieval-augmented generation (RAG) techniques have emerged as a promising solution to enhance the reliability of large language models (LLMs) by addressing issues like hallucinations, outdated knowledge, and domain adaptation. In…
Scientific discovery catalyzes human intellectual advances, driven by the cycle of hypothesis generation, experimental design, evaluation, and assumption refinement. Central to this process is causal inference, uncovering the mechanisms…
We consider the task of constructing a data structure for associating a static set of keys with values, while allowing arbitrary output values for queries involving keys outside the set. Compared to hash tables, these so-called static…
Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which…