Related papers: Data linkage algebra, data linkage dynamics, and p…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
With the advancement of robotics, machine learning, and machine perception, increasingly more robots will enter human environments to assist with daily tasks. However, dynamically-changing human environments requires reactive motion plans.…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Systematicity, i.e., the ability to recombine known parts and rules to form new sequences while reasoning over relational data, is critical to machine intelligence. A model with strong systematicity is able to train on small-scale tasks and…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
We present an experimental recipe for studying the relationship between training data and language model (LM) behavior. We outline steps for intervening on data batches -- i.e., ``rewriting history'' -- and then retraining model checkpoints…
Recently, Gavazzo has developed a relational theory of symbolic manipulation, that allows to study syntax-based rewriting systems without relying on specific notions of syntax. This theory was obtained by extending the algebra of relations…
Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which…
In this paper we propose a logic-based, framework inspired by artificial intelligence, but scaled down for practical database and programming applications. Computation in the framework is viewed as the task of generating a sequence of state…
With the needs of science and business, data sharing and re-use has become an intensive activity for various areas. In many cases, governance imposes rules concerning data use, but there is no existing computational technique to help…
Data is the key asset for organizations and data sharing is lifeline for organization growth; which may lead to data loss. Data leakage is the most critical issue being faced by organizations. In order to mitigate the data leakage issues…
Among the multiple causes of high error rates in spreadsheets, lack of proper training and of deep understanding of the computational model upon which spreadsheet computations rest might not be the least issue. The paper addresses this…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular,…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control.…
Entity Linking involves detecting and linking entity mentions in natural language texts to a knowledge graph. Traditional methods use a two-step process with separate models for entity recognition and disambiguation, which can be…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.