Related papers: Thin Coalgebraic Behaviours Are Inductive

An old theorem of Ad\'amek constructs initial algebras for sufficiently cocontinuous endofunctors via transfinite iteration over ordinals in classical set theory. We prove a new version that works in constructive logic, using "inflationary"…

Imitation learning, which learns agent policy by mimicking expert demonstration, has shown promising results in many applications such as medical treatment regimes and self-driving vehicles. However, it remains a difficult task to interpret…

We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then…

We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…

We study the monoid of so called projection functors $\p{S}$ attached to simple modules $S$ of a finite dimensional algebra, which appear naturally in the study of torsion pairs. We determine defining relations in special cases of path…

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

Motivated by recent work on weak distributive laws and their applications to coalgebraic semantics, we investigate the algebraic nature of semialgebras for a monad. These are algebras for the underlying functor of the monad subject to the…

The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…

Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…

Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition…

We explore links between the thin concurrent games of Castellan, Clairambault and Winskel, and the weighted relational models of linear logic studied by Laird, Manzonetto, McCusker and Pagani. More precisely, we show that there is an…

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…

We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of…

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and…