Related papers: Category-Theoretical and Topos-Theoretical Framewo…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Over the past decade, deep neural networks have demonstrated significant success using the training scheme that involves mini-batch stochastic gradient descent on extensive datasets. Expanding upon this accomplishment, there has been a…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…

Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a…

How can we discover and succinctly summarize the concepts that a neural network has learned? Such a task is of great importance in applications of networks in areas of inference that involve classification, like medical diagnosis based on…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…

Online learning represents an important family of machine learning algorithms, in which a learner attempts to resolve an online prediction (or any type of decision-making) task by learning a model/hypothesis from a sequence of data…

This survey paper presents a comprehensive analysis of crime prediction methodologies, exploring the various techniques and technologies utilized in this area. The paper covers the statistical methods, machine learning algorithms, and deep…

Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…

Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance…

Continual learning, also known as incremental learning or life-long learning, stands at the forefront of deep learning and AI systems. It breaks through the obstacle of one-way training on close sets and enables continuous adaptive learning…

Although principles of neuroscience like reinforcement learning, visual perception and attention have been applied in machine learning models, there is a huge gap between machine learning and mammalian learning. Based on the advances in…

Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…

Machine learning systems often do not share the same inductive biases as humans and, as a result, extrapolate or generalize in ways that are inconsistent with our expectations. The trade-off between exemplar- and rule-based generalization…

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…