Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions

We examine a private ADMM variant for (strongly) convex objectives which is a primal-dual iterative method. Each iteration has a user with a private function used to update the primal variable, masked by Gaussian noise for local privacy, without directly adding noise to the dual variable. Privacy amplification by iteration explores if noises from later iterations can enhance the privacy guarantee when releasing final variables after the last iteration. Cyffers et al. [ICML 2023] explored privacy amplification by iteration for the proximal ADMM variant, where a user's entire private function is accessed and noise is added to the primal variable. In contrast, we examine a private ADMM variant requiring just one gradient access to a user's function, but both primal and dual variables must be passed between successive iterations. To apply Balle et al.'s [NeurIPS 2019] coupling framework to the gradient ADMM variant, we tackle technical challenges with novel ideas. First, we address the non-expansive mapping issue in ADMM iterations by using a customized norm. Second, because the dual variables are not masked with any noise directly, their privacy guarantees are achieved by treating two consecutive noisy ADMM iterations as a Markov operator. Our main result is that the privacy guarantee for the gradient ADMM variant can be amplified proportionally to the number of iterations. For strongly convex objective functions, this amplification exponentially increases with the number of iterations. These amplification results align with the previously studied special case of stochastic gradient descent.

Efficient Numerical Algorithm for Large-Scale Damped Natural Gradient Descent

We propose a new algorithm for efficiently solving the damped Fisher matrix in large-scale scenarios where the number of parameters significantly exceeds the number of available samples. This problem is fundamental for natural gradient descent and stochastic reconfiguration. Our algorithm is based on Cholesky decomposition and is generally applicable. Benchmark results show that the algorithm is significantly faster than existing methods.

Enhancing Spectrum Sensing via Reconfigurable Intelligent Surfaces: Passive or Active Sensing and How Many Reflecting Elements are Needed?

Cognitive radio has been proposed to alleviate the scarcity of available spectrum. However, sensing performance is quite poor due to the low sensing signal-to-noise ratio. Fortunately, reconfigurable intelligent surface (RIS)-aided spectrum sensing can effectively tackle the above challenge due to its high array gain. Nevertheless, the traditional passive RIS suffers from the ``double fading'' effect, which severely restricts the performance of passive RIS-aided spectrum sensing. To this end, we introduce the active RIS into spectrum sensing and respectively formulate two optimization problems for the passive RIS and the active RIS to maximize the detection probability. In light of the intractability of the formulated problems, we develop a one-stage optimization algorithm with inner approximation and a two-stage optimization algorithm with a bisection method to obtain sub-optimal solutions, and apply the Rayleigh quotient to obtain the upper and lower bounds of the detection probability. Furthermore, in order to gain more insight into the impact of the RIS on spectrum sensing, we respectively investigate the number configuration for passive RIS and active RIS and analyze how many reflecting elements are needed to achieve the detection probability close to 1. Simulation results verify the effectiveness of the proposed algorithms.

Computation-Efficient Backscatter-Blessed MEC with User Reciprocity

This letter proposes a new user cooperative offloading protocol called user reciprocity in backscatter communication (BackCom)-aided mobile edge computing systems with efficient computation, whose quintessence is that each user can switch alternately between the active or the BackCom mode in different slots, and one user works in the active mode and the other user works in the BackCom mode in each time slot. In particular, the user in the BackCom mode can always use the signal transmitted by the user in the active mode for more data transmission in a spectrum-sharing manner. To evaluate the proposed protocol, a computation efficiency (CE) maximization-based optimization problem is formulated by jointly power control, time scheduling, reflection coefficient adjustment, and computing frequency allocation, while satisfying various physical constraints on the maximum energy budget, the computing frequency threshold, the minimum computed bits, and harvested energy threshold. To solve this non-convex problem, Dinkelbach's method and quadratic transform are first employed to transform the complex fractional forms into linear ones. Then, an iterative algorithm is designed by decomposing the resulting problem to obtain the suboptimal solution. The closed-form solutions for the transmit power, the RC, and the local computing frequency are provided for more insights. Besides, the analytical performance gain with the reciprocal mode is also derived. Simulation results demonstrate that the proposed scheme outperforms benchmark schemes regarding the CE.

To Reflect or Not To Reflect: On-Off Control and Number Configuration for Reflecting Elements in RIS-Aided Wireless Systems

Reconfigurable intelligent surface (RIS) has been regarded as a promising technique due to its high array gain and low power. However, the traditional passive RIS suffers from the ``double fading'' effect, which has restricted the performance of passive RIS-aided communications. Fortunately, active RIS can alleviate this problem since it can adjust the phase shift and amplify the received signal simultaneously. Nevertheless, a high beamforming gain often requires a number of reflecting elements, which leads to non-negligible power consumption, especially for the active RIS. Thus, one challenge is how to improve the scalability of the RIS and the energy efficiency. Different from the existing works where all reflecting elements are activated, we propose a novel element on-off mechanism where reflecting elements can be flexibly activated and deactivated. Two different optimization problems for passive RIS and active RIS are formulated by maximizing the total energy efficiency. We develop two different alternating optimization-based iterative algorithms to obtain sub-optimal solutions. Furthermore, we consider special cases involving rate maximization problems for given the same total power budget, and respectively analyze the number configuration for passive RIS and active RIS. Simulation results verify that reflecting elements under the proposed algorithms can be flexibly activated and deactivated.

Exploring Hybrid Active-Passive RIS-Aided MEC Systems: From the Mode-Switching Perspective

Mobile edge computing (MEC) has been regarded as a promising technique to support latencysensitivity and computation-intensive serves. However, the low offloading rate caused by the random channel fading characteristic becomes a major bottleneck in restricting the performance of the MEC. Fortunately, reconfigurable intelligent surface (RIS) can alleviate this problem since it can boost both the spectrum- and energy- efficiency. Different from the existing works adopting either fully active or fully passive RIS, we propose a novel hybrid RIS in which reflecting units can flexibly switch between active and passive modes. To achieve a tradeoff between the latency and energy consumption, an optimization problem is formulated by minimizing the total cost. In light of the intractability of the problem, we develop an alternating optimization-based iterative algorithm by combining the successive convex approximation method, the variable substitution, and the singular value decomposition (SVD) to obtain sub-optimal solutions. Furthermore, in order to gain more insight into the problem, we consider two special cases involving a latency minimization problem and an energy consumption minimization problem, and respectively analyze the tradeoff between the number of active and passive units. Simulation results verify that the proposed algorithm can achieve flexible mode switching and significantly outperforms existing algorithms.

Gain without Pain: Recycling Reflected Energy from Wireless Powered RIS-aided Communications

In this paper, we investigate and analyze energy recycling for a reconfigurable intelligent surface (RIS)-aided wireless-powered communication network. As opposed to the existing works where the energy harvested by Internet of things (IoT) devices only come from the power station, IoT devices are also allowed to recycle energy from other IoT devices. In particular, we propose group switching- and user switching-based protocols with time-division multiple access to evaluate the impact of energy recycling on system performance. Two different optimization problems are respectively formulated for maximizing the sum throughput by jointly optimizing the energy beamforming vectors, the transmit power, the transmission time, the receive beamforming vectors, the grouping factors, and the phase-shift matrices, where the constraints of the minimum throughput, the harvested energy, the maximum transmit power, the phase shift, the grouping, and the time allocation are taken into account. In light of the intractability of the above problems, we respectively develop two alternating optimization-based iterative algorithms by combining the successive convex approximation method and the penalty-based method to obtain corresponding sub-optimal solutions. Simulation results verify that the energy recycling-based mechanism can assist in enhancing the performance of IoT devices in terms of energy harvesting and information transmission. Besides, we also verify that the group switching-based algorithm can improve more sum throughput of IoT devices, and the user switching-based algorithm can harvest more energy.

A deep variational free energy approach to dense hydrogen

We present a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wavefunction at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. Our result suggests that hydrogen in the planetary condition is even denser compared to previous Monte Carlo and ab initio molecular dynamics data, which is further away from the empirical chemical model predictions. Obtaining reliable equations of state of dense hydrogen, and in particular, direct access to entropy and free energy opens new opportunities in planetary modeling and high-pressure physics research.

$m^\ast$ of two-dimensional electron gas: a neural canonical transformation study

The quasiparticle effective mass $m^\ast$ of interacting electrons is a fundamental quantity in the Fermi liquid theory. However, the precise value of the effective mass of uniform electron gas is still elusive after decades of research. The newly developed neural canonical transformation approach arXiv:2105.08644 offers a principled way to extract the effective mass of electron gas by directly calculating the thermal entropy at low temperature. The approach models a variational many-electron density matrix using two generative neural networks: an autoregressive model for momentum occupation and a normalizing flow for electron coordinates. Our calculation reveals a suppression of effective mass in the two-dimensional spin-polarized electron gas, which is more pronounced than previous reports in the low-density strong-coupling region. This prediction calls for verification in two-dimensional electron gas experiments.

Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.