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Optimal feedback control (OFC) is a theory from the motor control literature that explains how humans move their body to achieve a certain goal, e.g., pointing with the finger. OFC is based on the assumption that humans aim to control their body optimally, within the constraints imposed by body, environment, and task. In this paper, we explain how this theory can be applied to understanding Human-Computer Interaction (HCI) in the case of pointing. We propose that the human body and computer dynamics can be interpreted as a single dynamical system. The system state is controlled by the user via muscle control signals, and estimated from observations. Between-trial variability arises from signal-dependent control noise and observation noise. We compare four different models from optimal control theory and evaluate to what degree these models can replicate movements in the case of mouse pointing. We introduce a procedure to identify parameters that best explain observed user behavior. To support HCI researchers in simulating, analyzing, and optimizing interaction movements, we provide the Python toolbox OFC4HCI. We conclude that OFC presents a powerful framework for HCI to understand and simulate motion of the human body and of the interface on a moment by moment basis.

Mobile devices have been manufactured and enhanced at growing rates in the past decades. While this growth has significantly evolved the capability of these devices, their security has been falling behind. This contrast in development between capability and security of mobile devices is a significant problem with the sensitive information of the public at risk. Continuing the previous work in this field, this study identifies key Machine Learning algorithms currently being used for behavioral biometric mobile authentication schemes and aims to provide a comprehensive review of these algorithms when used with touch dynamics and phone movement. Throughout this paper the benefits, limitations, and recommendations for future work will be discussed.

In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that considering a time discretization with a positive step size $h$ an error bound of size $h$ can be proved for the difference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) and the value function of the discrete time problem. However, including also a spatial discretization based on elements of size $k$ an error bound of size $O(k/h)$ can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under similar assumptions to those of the time discrete case, that the error of the fully discrete case is in fact $O(h+k)$ which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behaviour $1/h$ from the bound $O(k/h)$ have not been observed.

We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.

Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it is difficult to directly discuss the search behavior of an intelligent optimization algorithm, since there are so many kinds of intelligent schemes. To address this problem, an intelligent optimization system is regarded as a simulated physical optimization system in this paper. The dynamic search behavior of such a simplified physical optimization system are investigated with quantum theory. To achieve this goal, the Schroedinger equation is employed as the dynamics equation of the optimization algorithm, which is used to describe dynamic search behaviours in the evolution process with quantum theory. Moreover, to explore the basic behaviour of the optimization system, the optimization problem is assumed to be decomposed and approximated. Correspondingly, the basic search behaviour is derived, which constitutes the basic iterative process of a simple optimization system. The basic iterative process is compared with some classical bare-bones schemes to verify the similarity of search behavior under different metaphors. The search strategies of these bare bones algorithms are analyzed through experiments.

After spending 9 years in Quantum Computing and given the impending timeline of developing good quality quantum processing units, it is the moment to rethink the approach to advance quantum computing research. Rather than waiting for quantum hardware technologies to mature, we need to start assessing in tandem the impact of the occurrence of quantum computing in various scientific fields. However, for this purpose, we need to use a complementary but quite different approach than proposed by the NISQ vision, which is heavily focused on and burdened by the engineering challenges. That is why we propose and advocate the PISQ-approach: Perfect Intermediate-Scale Quantum computing based on the already known concept of perfect qubits. This will allow researchers to focus much more on the development of new applications by defining the algorithms in terms of perfect qubits and evaluating them on quantum computing simulators that are executed on supercomputers. It is not a long-term solution but it will allow universities to currently develop research on quantum logic and algorithms and companies can already start developing their internal know-how on quantum solutions.

Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature is becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, Chignolin and Bovine Pancreatic Trypsin Inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.