相关论文: The Ramanujan Library -- Automated Discovery on th…

In this paper, we propose a Retrieval Augmented Generation (RAG) agent that maps natural language queries about research topics to precise, machine-interpretable semantic entities. Our approach combines RAG with Socratic dialogue to align a…

Querying is one of the basic functionality expected from a database system. Query efficiency is adversely affected by increase in the number of participating tables. Also, querying based on syntax largely limits the gamut of queries a…

Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…

Context graphs are essential for modern AI applications including question answering, pattern discovery, and data analysis. Building accurate context graphs from structured databases requires inferring join relationships between entities.…

Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of…

Vast amounts of heterogeneous knowledge are becoming publicly available in the form of knowledge graphs, often linking multiple sources of data that have never been together before, and thereby enabling scholars to answer many new research…

Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing…

Identifying and predicting the factors that contribute to the success of interdisciplinary research is crucial for advancing scientific discovery. However, there is a lack of methods to quantify the integration of new ideas and…

Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…

Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…

Mathematical knowledge exists in many forms, ranging from informal textbooks and lecture notes to large formal proof libraries, yet moving between these representations remains difficult. Informal texts hide dependencies, while formal…

Link prediction infers missing or future relations between graph nodes, based on connection patterns. Scientific literature networks and knowledge graphs are typically large, sparse, and noisy, and often contain missing links between…

Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…

In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…

What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs? What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

The evaluation of mathematical results plays a central role in assessing researchers' contributions and shaping the direction of the field. Currently, such evaluations rely primarily on human judgment, whether through journal peer review or…

There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln…

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…