相关论文: The Ramanujan Library -- Automated Discovery on th…
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
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.…
Persistent memory is a central capability for AI agents, yet the mathematical foundations of memory retrieval, lifecycle management, and consistency remain unexplored. Current systems employ cosine similarity for retrieval, heuristic decay…
Skill libraries enable large language model agents to reuse experience from past interactions, but most existing libraries store skills as isolated entries and retrieve them only by semantic similarity. This leads to two key challenges for…
The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we…
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
The goal of case-based retrieval is to assist physicians in the clinical decision making process, by finding relevant medical literature in large archives. We propose a research that aims at improving the effectiveness of case-based…
During the past decade, there has been an extensive investigation of the computational complexity of the consistent answers of Boolean conjunctive queries under primary key constraints. Much of this investigation has focused on…
We address the fundamental task of inferring cross-document coreference and hierarchy in scientific texts, which has important applications in knowledge graph construction, search, recommendation and discovery. Large Language Models (LLMs)…
Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In…
Large language models record impressive performance on many natural language processing tasks. However, their knowledge capacity is limited to the pretraining corpus. Retrieval augmentation offers an effective solution by retrieving context…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…
Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous…
In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable…
Range-filtered approximate nearest neighbor (RFANN) search is a fundamental operation in modern data systems. Given a set of objects, each with a vector and a numerical attribute, an RFANN query retrieves the nearest neighbors to a query…