Related papers: Betwixt Turing and Kleene
A core challenge in Machine Learning is to learn to disentangle natural factors of variation in data (e.g. object shape vs. pose). A popular approach to disentanglement consists in learning to map each of these factors to distinct subspaces…
We propose Token Turing Machines (TTM), a sequential, autoregressive Transformer model with memory for real-world sequential visual understanding. Our model is inspired by the seminal Neural Turing Machine, and has an external memory…
By closely rereading the original Turing's 1936 article, we can gain insight about that it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
DEKL 2.0 is a dependent type-theoretic framework for trace-indexed knowledge evolution. Its central claim is that the proof calculus remains monotone under standard structural rules, while non-monotonic behavior arises semantically from…
With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
The supersymmetric reformulation of physical observables in the Chalker-Coddington model (CC) for the plateau transition in the integer quantum Hall effect leads to a reformulation of its critical properties in terms of a 2D non-compact…
A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
We study functions from reals to reals which are uniformly degree-invariant from Turing-equivalence to many-one equivalence, and compare them "on a cone." We prove that they are in one-to-one correspondence with the Wadge degrees, which can…
Some notions in mathematics can be considered relative. Relative is a term used to denote when the variation in the position of an observer implies variation in properties or measures on the observed object. We know, from Skolem theorem,…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
It is known that there exist mathematical problems of practical relevance which cannot be computed on a Turing machine. An important example is the calculation of the first derivative of continuously differentiable functions. This paper…
Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our…