Related papers: Hypocomputation
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
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…
High Performance Computing (HPC) aims at providing reasonably fast computing solutions to scientific and real life problems. The advent of multicore architectures is noticeable in the HPC history, because it has brought the underlying…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
Present day mathematics is a human construct, where computers are used more and more but do not play a creative role. This situation may change however: computers may become creative, and since they function very differently from the human…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…