Related papers: Smooth relaxation preserving Turing machines
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
Overconfidence has been shown to impair generalization and calibration of a neural network. Previous studies remedy this issue by adding a regularization term to a loss function, preventing a model from making a peaked distribution. Label…
Spatial control of topology is highly desirable for realizing tunable quantum functionalities in materials. Moir\'e superlattices formed by twisting van der Waals heterostructures provide a natural platform for spatially modulated…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
Despite a cost-effective option in practical engineering, Reynolds-averaged Navier-Stokes simulations are facing the ever-growing demand for more accurate turbulence models. Recently, emerging machine learning techniques are making…
As an example of the concept of rulial space, we explore the case of simple Turing machines. We construct the rulial multiway graph which represents the behavior of all possible Turing machines with a certain class of rules. This graph…
Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque.…
Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory…
Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems.…
Data noising is an effective technique for regularizing neural network models. While noising is widely adopted in application domains such as vision and speech, commonly used noising primitives have not been developed for discrete…
We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence with limited…
Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper…
Upon quenching the forcing, a turbulent system tends to attain the state of stable equilibrium through the process of turbulent relaxation. Such relaxation in binary fluids is of surmount interest for both fundamental science understanding…
This paper considers the computational power of constant size, dynamic Bayesian networks. Although discrete dynamic Bayesian networks are no more powerful than hidden Markov models, dynamic Bayesian networks with continuous random variables…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
Introduction of a twist between layers of two-dimensional materials which leads to the formation of a moir\'e pattern is an emerging pathway to tune the electronic, vibrational and optical properties. The fascinating properties of these…
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…