Related papers: Reversible effects as inverse arrows
The humble $\dagger$ ("dagger") is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains).…
Reversible computation is an unconventional form of computing where any executed sequence of operations can be executed in reverse at any point during computation. It has recently been attracting increasing attention in various research…
We introduce a new programming language and its categorical semantics in order to design and implement neural networks within the framework of algebraic effects and handlers for arrows. Our language enables us to construct neural networks…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian…
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…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Guarded recursion is a framework allowing for a formalisation of streams in classical programming languages. The latter take their semantics in cartesian closed categories. However, some programming paradigms do not take their semantics in…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for…
Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key…
In system operations it is commonly assumed that arbitrary changes to a system can be reversed or `rolled back', when errors of judgement and procedure occur. We point out that this view is flawed and provide an alternative approach to…
Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This recipe effectively constructs a…
Reversible computing is a computational paradigm in which computations are deterministic in both the forward and backward direction, so that programs have well-defined forward and backward semantics. We investigate the formal semantics of…
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…
Reversing a (forward) computation history means undoing the history. In concurrent systems, undoing the history is not performed in a deterministic way but in a causally consistent fashion, where states that are reached during a backward…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this…
We show that the model of quantum computation based on density matrices and superoperators can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be…