arXiv subjects

Xin Guo

Publications and source records attributed to Xin Guo.

At least 127 records · Page 7Linked to original sources

arXiv2023

High-speed 4 ${\times}$ 4 silicon photonic electro-optic switch, operating at the 2 μm waveband

The escalating need for expansive data bandwidth, and the resulting capacity constraints of the single mode fiber (SMF) have positioned the 2-$μ$m waveband as a prospective window for emerging applications in optical communication. This has initiated an ecosystem of silicon photonic components in the region driven by CMOS compatibility, low cost, high efficiency and potential for large-scale integration. In this study, we demonstrate a plasma dispersive, 4 ${\times}$ 4 electro-optic switch operating at the 2-$μ$m waveband with the shortest switching times. The demonstrated switch operates across a 45-nm bandwidth, with 10-90% rise and 90-10% fall time of 1.78 ns and 3.02 ns respectively. In a 4 ${\times}$ 4 implementation, crosstalk below -15 dB and power consumption below 19.15 mW across all 16 ports are indicated. The result brings high-speed optical switching to the portfolio of devices at the promising waveband.

physics.optics↗

arXiv2023

Vacuum torque, propulsive forces, and anomalous tangential forces: Effects of nonreciprocal media out of thermal equilibrium

From the generalized fluctuation-dissipation theorem, it is known that a body at rest made of nonreciprocal material may experience a torque, even in vacuum, if it is not in thermal equilibrium with its environment. However, it does not experience self-propulsion in such circumstances, except in higher order. Nevertheless, such a body may experience both a normal torque and a lateral force when adjacent to an ordinary surface with transverse translational symmetry. We explore how these phenomena arise, discuss what terminal velocities might be achieved, and point out some of the limitations of applying our results to observations, including the Lorenz-Lorentz correction, and the cooling due to radiation. In spite of these limitations, the effects discussed would seem to be observable.

quant-ph↗

arXiv2023

Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation

Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper establishes a continuous-time approximation for the mini-max game of adversarial training. This approximation approach allows for precise and analytical comparisons between stochastic gradient descent and its adversarial training counterpart; and confirms theoretically the robustness of adversarial training from a new gradient-flow viewpoint. The analysis is then corroborated through various analytical and numerical examples.

cs.LG↗

arXiv2023

Feasibility of Transfer Learning: A Mathematical Framework

Transfer learning is a popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. It has enjoyed numerous empirical successes and inspired a growing number of theoretical studies. This paper addresses the feasibility issue of transfer learning. It begins by establishing the necessary mathematical concepts and constructing a mathematical framework for transfer learning. It then identifies and formulates the three-step transfer learning procedure as an optimization problem, allowing for the resolution of the feasibility issue. Importantly, it demonstrates that under certain technical conditions, such as appropriate choice of loss functions and data sets, an optimal procedure for transfer learning exists. This study of the feasibility issue brings additional insights into various transfer learning problems. It sheds light on the impact of feature augmentation on model performance, explores potential extensions of domain adaptation, and examines the feasibility of efficient feature extractor transfer in image classification.

cs.LG↗

arXiv2023

Quantum friction in the presence of a perfectly conducting plate

A neutral but polarizable particle at rest near a perfectly conducting plate feels a force normal to the surface of the plate, which tends to pull the particle towards the plate. This is the well-known Casimir-Polder force, which has long been theoretically proposed and experimentally observed. In this paper, we explore the transverse frictional force on an atom moving uniformly parallel to a perfectly conducting plate. Although many theoretical predictions can be found for the quantum friction on a particle moving above an imperfect surface, the extreme situation with a perfectly conducting plate seems to have been largely ignored by the theoretical community. We investigate this ideal case as a natural extension of our previous works on quantum vacuum friction (blackbody friction), and conclude that there does exist a quantum frictional force on an atom moving above a perfectly conducting plate. Very interestingly, the distance dependence, the temperature dependence and even the sign of the frictional force can depend on the polarization state of the atom. For an isotropic atom with a static polarizability, the resultant frictional force is found to be negative definite and therefore remains a true drag. Just above the surface of the plate, the magnitude of the frictional force is twice that of the quantum vacuum friction in the absence of the plate.

quant-ph↗

arXiv2023

Feasibility and Transferability of Transfer Learning: A Mathematical Framework

Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. Despite its numerous empirical successes, theoretical analysis for transfer learning is limited. In this paper we build for the first time, to the best of our knowledge, a mathematical framework for the general procedure of transfer learning. Our unique reformulation of transfer learning as an optimization problem allows for the first time, analysis of its feasibility. Additionally, we propose a novel concept of transfer risk to evaluate transferability of transfer learning. Our numerical studies using the Office-31 dataset demonstrate the potential and benefits of incorporating transfer risk in the evaluation of transfer learning performance.

cs.LG↗

arXiv2023

A General Framework for Learning Mean-Field Games

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and demonstrates that naively combining reinforcement learning with the fixed-point approach in classical MFGs yields unstable algorithms. It then proposes value-based and policy-based reinforcement learning algorithms (GMF-V and GMF-P, respectively) with smoothed policies, with analysis of their convergence properties and computational complexities. Experiments on an equilibrium product pricing problem demonstrate that GMF-V-Q and GMF-P-TRPO, two specific instantiations of GMF-V and GMF-P, respectively, with Q-learning and TRPO, are both efficient and robust in the GMFG setting. Moreover, their performance is superior in convergence speed, accuracy, and stability when compared with existing algorithms for multi-agent reinforcement learning in the $N$-player setting.

cs.LG↗

arXiv2022

Optimization frameworks and sensitivity analysis of Stackelberg mean-field games

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to maximize her reward considering the worst-case cost over all possible $ε$-Nash equilibria among followers. A new analytical paradigm is established by showing the equivalence between this Stackelberg mean-field game and a minimax optimization problem. This optimization framework facilitates studying both analytically and numerically the set of Nash equilibria for the game; and leads to the sensitivity and the robustness analysis of the game value. In particular, when there is model uncertainty, the game value for the leader suffers non-vanishing sub-optimality as the perturbed model converges to the true model. In order to obtain a near-optimal solution, the leader needs to be more pessimistic with anticipation of model errors and adopts a relaxed version of the original Stackelberg game.

math.OC↗

arXiv2022

Capacity dependent analysis for functional online learning algorithms

This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the sampling process covariance operator, significant improvement on the convergence rates is achieved. Both prediction problems and estimation problems are studied, where we show that capacity assumption can alleviate the saturation of the convergence rate as the regularity of the target function increases. We show that with properly selected kernel, capacity assumptions can fully compensate for the regularity assumptions for prediction problems (but not for estimation problems). This demonstrates the significant difference between the prediction problems and the estimation problems in functional data analysis.

stat.ML↗

arXiv2022

Itô's formula for flows of measures on semimartingales

We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô's formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques. This general form of Itô's formula enables the derivation of dynamic programming equations and verification theorems for McKean--Vlasov controls with jump diffusions and for McKean--Vlasov mixed regular-singular control problems. It also allows for generalizing the classical relationship between the maximum principle and the dynamic programming principle to the McKean--Vlasov singular control setting, where the adjoint process is expressed in terms of the derivative of the value function with respect to the probability measures.

math.PR↗

arXiv2022

Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon

We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm based on continuous-time observations and controls, and establish a logarithmic regret bound of order $O((\ln M)(\ln\ln M))$, with $M$ being the number of learning episodes. The analysis consists of two parts: perturbation analysis, which exploits the regularity and robustness of the associated Riccati differential equation; and parameter estimation error, which relies on sub-exponential properties of continuous-time least-squares estimators. We further propose a practically implementable least-squares algorithm based on discrete-time observations and piecewise constant controls, which achieves similar logarithmic regret with an additional term depending explicitly on the time stepsizes used in the algorithm.

math.OC↗

arXiv2022

Approximation of N-player stochastic games with singular controls by mean field games

This paper establishes that a class of $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows (i) the optimal control to an MFG with singular controls of a bounded velocity $θ$ is shown to be an $ε_N$-NE to an $N$-player game with singular controls of the bounded velocity, with $ε_N = O(\frac{1}{\sqrt{N}})$, and (ii) the optimal control to this MFG is an $(ε_N + ε_θ)$-NE to an $N$-player game with singular controls of finite variation, where $ε_θ$ is an error term that depends on $θ$. This work generalizes the classical result on approximation $N$-player games by MFGs, by allowing for discontinuous controls.

math.OC↗

arXiv2022

Casimir Self-Entropy of Nanoparticles with Classical Polarizabilities: Electromagnetic Field Fluctuations

Not only are Casimir interaction entropies not guaranteed to be positive, but also, more strikingly, Casimir self-entropies of bodies can be negative. Here, we attempt to interpret the physical origin and meaning of these negative self-entropies by investigating the Casimir self-entropy of a neutral spherical nanoparticle. After extracting the polarizabilities of such a particle by examining the asymptotic behavior of the scattering Green's function, we compute the corresponding free energy and entropy. Two models for the nanoparticle, namely a spherical plasma $δ$-function shell and a homogeneous dielectric/diamagnetic ball, are considered at low temperature, because that is all that can be revealed from a nanoparticle perspective. The second model includes a contribution to the entropy from the bulk free energy, referring to the situation where the medium inside or outside the ball fills all space, which must be subtracted on physical grounds in order to maintain consistency with van der Waals interactions, corresponding to the self-entropy of each bulk. (The van der Waals calculation is described in Appendix A.) The entropies so calculated agree with known results in the low-temperature limit, appropriate for a small particle, and are negative. But we suggest that the negative self-entropy is simply an interaction entropy, the difference between the total entropy and the blackbody entropy of the two bulks, outside or inside of the nanosphere. The vacuum entropy is always positive and overwhelms the interaction entropy. Thus the interaction entropy can be negative, without contradicting the principles of statistical thermodynamics. Because the entropy of blackbody radiation by itself plays an important role, it is also discussed, including dispersive effects, in detail.

hep-th↗

arXiv2022

Energetics of quantum vacuum friction. II: Dipole fluctuations and field fluctuations

As a second paper in series with arXiv:2108.01539, we discuss here quantum vacuum friction on an intrinsically dissipative particle. The friction arises not only from the field fluctuations but also from the dipole fluctuations intrinsic to the particle. As a result, the dissipative particle can be out of the nonequilibrium steady state (NESS), where it loses or gains internal energy. Only if the temperature of the particle equals a special NESS temperature will the particle be in NESS. We first derive the NESS conditions which give the NESS temperature of the particle as a function of the radiation temperature and the velocity of the particle. Imposing the NESS conditions, we then obtain an expression for the quantum vacuum friction in NESS. The NESS quantum vacuum friction is shown to be always negative definite, therefore a true drag. The NESS temperature and quantum vacuum friction are calculated numerically for various models. Out of NESS, even though the quantum vacuum frictional force no longer has a definite sign in the rest frame of the radiation, we find the external force needed to keep the particle moving must be in the same direction as the motion of the particle. This then excludes the possibility of making a perpetual motion machine, which could convert the vacuum energy into useful mechanical work. In addition, we find that the deviation of the temperature of the particle from its NESS temperature causes the particle to lose or gain internal energy in such a way that the particle would return to NESS after deviating from it. This enables experimental measurements of the NESS temperature of the particle to serve as a feasible signature for these quantum vacuum frictional effects.

hep-th↗

arXiv2022

Dynamic Programming Principles for Mean-Field Controls with Learning

Dynamic programming principle (DPP) is fundamental for control and optimization, including Markov decision problems (MDPs), reinforcement learning (RL), and more recently mean-field controls (MFCs). However, in the learning framework of MFCs, DPP has not been rigorously established, despite its critical importance for algorithm designs. In this paper, we first present a simple example in MFCs with learning where DPP fails with a mis-specified Q function; and then propose the correct form of Q function in an appropriate space for MFCs with learning. This particular form of Q function is different from the classical one and is called the IQ function. In the special case when the transition probability and the reward are independent of the mean-field information, it integrates the classical Q function for single-agent RL over the state-action distribution. In other words, MFCs with learning can be viewed as lifting the classical RLs by replacing the state-action space with its probability distribution space. This identification of the IQ function enables us to establish precisely the DPP in the learning framework of MFCs. Finally, we illustrate through numerical experiments the time consistency of this IQ function.

math.OC↗

arXiv2022

Escaping Saddle Points Efficiently with Occupation-Time-Adapted Perturbations

Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the history of states via the notion of occupation time. After integrating this mechanism into the framework of perturbed gradient descent (PGD) and perturbed accelerated gradient descent (PAGD), two new algorithms are proposed: perturbed gradient descent adapted to occupation time (PGDOT) and its accelerated version (PAGDOT). PGDOT and PAGDOT are shown to converge to second-order stationary points at least as fast as PGD and PAGD, respectively, and thus they are guaranteed to avoid getting stuck at non-degenerate saddle points. The theoretical analysis is corroborated by empirical studies in which the new algorithms consistently escape saddle points and outperform not only their counterparts, PGD and PAGD, but also other popular alternatives including stochastic gradient descent, Adam, AMSGrad, and RMSProp.

math.OC↗

arXiv2022

Jitter-calibrated second-order correlation measurement of low-repetition-rate pulsed excitation

We report a new technique for the realization of second-order correlation ($g^2(τ)$) measurement under low-repetition-rate pulsed excitation (1 kHz), with timing jitter calibrated to restore lateral $g^2(τ)$ curves and determine $g^2(0)$. We use CdSe nanowire (NW) laser to demonstrate the jitter-calibrated $g^2(τ)$ measurement, where $g^2(0)$ evolution shows the laser emission transition process. The exciting pulses are split into reference and excitation channels, which enables the jitter calibration when the exciting pulses have significant timing jitter and low repetition rate. After using the reference signals to calibrate and rearrange the single-photon signals, lateral $g^2(τ)$ curves can be entirely restored, and $g^2(0)$ evolution is demonstrated from our method.

physics.optics↗

arXiv2022

Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls

We study finite-time horizon continuous-time linear-convex reinforcement learning problems in an episodic setting. In this problem, the unknown linear jump-diffusion process is controlled subject to nonsmooth convex costs. We show that the associated linear-convex control problems admit Lipchitz continuous optimal feedback controls and further prove the Lipschitz stability of the feedback controls, i.e., the performance gap between applying feedback controls for an incorrect model and for the true model depends Lipschitz-continuously on the magnitude of perturbations in the model coefficients; the proof relies on a stability analysis of the associated forward-backward stochastic differential equation. We then propose a novel least-squares algorithm which achieves a regret of the order $O(\sqrt{N\ln N})$ on linear-convex learning problems with jumps, where $N$ is the number of learning episodes; the analysis leverages the Lipschitz stability of feedback controls and concentration properties of sub-Weibull random variables. Numerical experiment confirms the convergence and the robustness of the proposed algorithm.

math.OC↗