Related papers: The Mathematical Abstraction Theory, The Fundament…

Real-world information networks are increasingly occurring across various disciplines including online social networks and citation networks. These network data are generally characterized by sparseness, nonlinearity and heterogeneity…

Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations.…

Knowledge discovery is defined as non-trivial extraction of implicit, previously unknown and potentially useful information from given data. Knowledge extraction from web documents deals with unstructured, free-format documents whose number…

Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…

Joint representation learning of text and knowledge within a unified semantic space enables us to perform knowledge graph completion more accurately. In this work, we propose a novel framework to embed words, entities and relations into the…

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

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…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

Neural network techniques are widely applied to obtain high-quality distributed representations of words, i.e., word embeddings, to address text mining, information retrieval, and natural language processing tasks. Recently, efficient…

The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…

This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…

Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and…

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…

Metaheuristics are widely recognized gradient-free solvers to hard problems that do not meet the rigorous mathematical assumptions of conventional solvers. The automated design of metaheuristic algorithms provides an attractive path to…

We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…

In sufficiently complex tasks, it is expected that as a side effect of learning to solve a problem, a neural network will learn relevant abstractions of the representation of that problem. This has been confirmed in particular in machine…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

This paper examines the connections among various approaches to understanding concepts in philosophy, cognitive science, and machine learning, with a particular focus on their mathematical nature. By categorizing these approaches into…

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…