Related papers: Descriptive inner model theory
We give describe several models for $(\infty,n)$-categories, with an emphasis on models given by diagrams of sets and simplicial sets. We look most closely at the cases when $n \leq 2$, then summarize methods of generalizing for all $n$.
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
This manifesto paper will introduce machine listening intelligence, an integrated research framework for acoustic and musical signals modelling, based on signal processing, deep learning and computational musicology.
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the…
This is the written version of a set of introductory lectures on string theory.
Decisions by humans depend on their estimations given some uncertain sensory data. These decisions can also be influenced by the behavior of others. Here we present a mathematical model to quantify this influence, inviting a further study…
Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What…
The paper continues the line of model-theoretic characterizations for versions of intuitionistic logic previously achieved by the author, further generalizing them. This results in a model-theoretic characterization of expressive powers of…
The dependency of the generalization error of neural networks on model and dataset size is of critical importance both in practice and for understanding the theory of neural networks. Nevertheless, the functional form of this dependency…
This paper aims to show that a simple framework, utilizing basic formalisms from set theory and category theory, can clarify and inform our theories of the relation between mind and matter.
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
The first objective of this paper are to introduce a strong theoretical concept as a proposed model that visualizes the process of realizing empathy, based on the ample analysis of the collected work in the survey. Secondly, the intended…
As Large Language Models (LLMs) become increasingly integrated into our daily lives, the potential harms from deceptive behavior underlie the need for faithfully interpreting their decision-making. While traditional probing methods have…
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
This article discuss a class of tractable model in the form of polynomial type.
This is a preliminary version of the Chapter 1 of a book "Computable Integrability"