Related papers: Convolution, Separation and Concurrency
Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
The evolution of cognition is frequently discussed as the evolution of cognitive abilities or the evolution of some neuronal structures in the brain. However, since such traits or abilities are often highly complex, understanding their…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
Using qualitative reasoning with geographic information, contrarily, for instance, with robotics, looks not only fastidious (i.e.: encoding knowledge Propositional Logics PL), but appears to be computational complex, and not tractable at…
Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group $G$ and a given normal subgroup $H$. We also give conditions for the existence of a…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Session types are a typed approach to message-passing concurrency, where types describe sequences of intended exchanges over channels. Session type systems have been given strong logical foundations via Curry-Howard correspondences with…
Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam…
Concurrent separation logic is distinguished by transfer of state ownership upon parallel composition and framing. The algebraic structure that underpins ownership transfer is that of partial commutative monoids (PCMs). Extant research…
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network…