Related papers: Nets and Reverse Mathematics, a pilot study

Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…

In this paper we consider the idea of I - convergence of nets of partial function from a metric space (X; d) to a metric space (Y; ?) and derive several basic characterization. This idea extends the concept of convergence of nets of partial…

Convergence spaces are a generalization of topological spaces. The category of convergence spaces is well-suited for Algebraic Topology, one of the reasons is the existence of exponential objects provided by continuous convergence. In this…

Teaching a computer to read and answer general questions pertaining to a document is a challenging yet unsolved problem. In this paper, we describe a novel neural network architecture called the Reasoning Network (ReasoNet) for machine…

The present paper deals with the question of representability of nets of C*-algebras whose underlying poset, indexing the net, is not upward directed. A particular class of nets, called C*-net bundles, is classified in terms of C*-dynamical…

Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…

The notion of minimal complements was introduced by Nathanson in 2011. Since then, the existence or the inexistence of minimal complements of sets have been extensively studied. Recently, the study of inverse problems, i.e., which sets can…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Given the ever-increasing computational costs of modern machine learning models, we need to find new ways to reuse such expert models and thus tap into the resources that have been invested in their creation. Recent work suggests that the…

Recent work has argued that neural networks can be understood theoretically by taking the number of channels to infinity, at which point the outputs become Gaussian process (GP) distributed. However, we note that infinite Bayesian neural…

Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly…

Heterogeneous network data with rich nodal information become increasingly prevalent across multidisciplinary research, yet accurately modeling complex nodal heterogeneity and simultaneously selecting influential nodal attributes remains an…

In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…

A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient…

A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Linear logic and the linear {\lambda}-calculus have a long standing tradition in the study of natural language form and meaning. Among the proof calculi of linear logic, proof nets are of particular interest, offering an attractive…

In this paper we propose a conceptual framework for higher-order artificial neural networks. The idea of higher-order networks arises naturally when a model is required to learn some group of transformations, every element of which is…