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The Gaussian Mechanism (GM), which consists in adding Gaussian noise to a vector-valued query before releasing it, is a standard privacy protection mechanism. In particular, given that the query respects some L2 sensitivity property (the L2 distance between outputs on any two neighboring inputs is bounded), GM guarantees R\'enyi Differential Privacy (RDP). Unfortunately, precisely bounding the L2 sensitivity can be hard, thus leading to loose privacy bounds. In this work, we consider a Relative L2 sensitivity assumption, in which the bound on the distance between two query outputs may also depend on their norm. Leveraging this assumption, we introduce the Relative Gaussian Mechanism (RGM), in which the variance of the noise depends on the norm of the output. We prove tight bounds on the RDP parameters under relative L2 sensitivity, and characterize the privacy loss incurred by using output-dependent noise. In particular, we show that RGM naturally adapts to a latent variable that would control the norm of the output. Finally, we instantiate our framework to show tight guarantees for Private Gradient Descent, a problem that naturally fits our relative L2 sensitivity assumption.

In this work, we address two limitations of existing conditional diffusion models: their slow inference speed due to the iterative denoising process and their reliance on paired data for model fine-tuning. To tackle these issues, we introduce a general method for adapting a single-step diffusion model to new tasks and domains through adversarial learning objectives. Specifically, we consolidate various modules of the vanilla latent diffusion model into a single end-to-end generator network with small trainable weights, enhancing its ability to preserve the input image structure while reducing overfitting. We demonstrate that, for unpaired settings, our model CycleGAN-Turbo outperforms existing GAN-based and diffusion-based methods for various scene translation tasks, such as day-to-night conversion and adding/removing weather effects like fog, snow, and rain. We extend our method to paired settings, where our model pix2pix-Turbo is on par with recent works like Control-Net for Sketch2Photo and Edge2Image, but with a single-step inference. This work suggests that single-step diffusion models can serve as strong backbones for a range of GAN learning objectives. Our code and models are available at //github.com/GaParmar/img2img-turbo.

In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis.

Motivated by the growing interest in correlation-robust stochastic optimization, we investigate stochastic selection problems beyond independence. Specifically, we consider the instructive case of pairwise-independent priors and matroid constraints. We obtain essentially-optimal bounds for contention resolution and prophet inequalities. The impetus for our work comes from the recent work of Caragiannis et al., who derived a constant-approximation for the single-choice prophet inequality with pairwise-independent priors. For general matroids, our results are tight and largely negative. For both contention resolution and prophet inequalities, our impossibility results hold for the full linear matroid over a finite field. We explicitly construct pairwise-independent distributions which rule out an omega(1/Rank)-balanced offline CRS and an omega(1/log Rank)-competitive prophet inequality against the (usual) oblivious adversary. For both results, we employ a generic approach for constructing pairwise-independent random vectors -- one which unifies and generalizes existing pairwise-independence constructions from the literature on universal hash functions and pseudorandomness. Specifically, our approach is based on our observation that random linear maps turn linear independence into stochastic independence. We then examine the class of matroids which satisfy the so-called partition property -- these include most common matroids encountered in optimization. We obtain positive results for both online contention resolution and prophet inequalities with pairwise-independent priors on such matroids, approximately matching the corresponding guarantees for fully independent priors. These algorithmic results hold against the almighty adversary for both problems.

We present JOG, a framework that facilitates developing Java JIT peephole optimizations alongside JIT tests. JOG enables developers to write a pattern, in Java itself, that specifies desired code transformations by writing code before and after the optimization, as well as any necessary preconditions. Such patterns can be written in the same way that tests of the optimization are already written in OpenJDK. JOG translates each pattern into C/C++ code that can be integrated as a JIT optimization pass. JOG also generates Java tests for optimizations from patterns. Furthermore, JOG can automatically detect possible shadow relation between a pair of optimizations where the effect of the shadowed optimization is overridden by another. Our evaluation shows that JOG makes it easier to write readable JIT optimizations alongside tests without decreasing the effectiveness of JIT optimizations. We wrote 162 patterns, including 68 existing optimizations in OpenJDK, 92 new optimizations adapted from LLVM, and two new optimizations that we proposed. We opened eight pull requests (PRs) for OpenJDK, including six for new optimizations, one on removing shadowed optimizations, and one for newly generated JIT tests; seven PRs have already been integrated into the master branch of OpenJDK.

In this work, we introduce an advanced thermo-active variable impedance module which builds upon our previous innovation in thermal-based impedance adjustment for actuation systems. Our initial design harnessed the temperature-responsive, viscoelastic properties of Polycaprolactone (PCL) to modulate stiffness and damping, facilitated by integrated flexible Peltier elements. While effective, the reliance on compressing and the inherent stress relaxation characteristics of PCL led to suboptimal response times in impedance adjustments. Addressing these limitations, the current iteration of our module pivots to a novel 'shear-mode' operation. By conducting comprehensive shear rheology analyses on PCL, we have identified a configuration that eliminates the viscoelastic delay, offering a faster response with improved heat transfer efficiency. A key advantage of our module lies in its scalability and elimination of additional mechanical actuators for impedance adjustment. The compactness and efficiency of thermal actuation through Peltier elements allow for significant downsizing, making these thermal, variable impedance modules exceptionally well-suited for applications where space constraints and actuator weight are critical considerations. This development represents a significant leap forward in the design of variable impedance actuators, offering a more versatile, responsive, and compact solution for a wide range of robotic and biomechanical applications.

In this work, we unveil the advantages of synergizing cooperative rate splitting (CRS) with user relaying and simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR RIS). Specifically, we propose a novel STAR RIS-assisted CRS transmission framework, featuring six unique transmission modes that leverage various combination of the relaying protocols (including full duplex-FD and half duplex-HD) and the STAR RIS configuration protocols (including energy splitting-ES, mode switching-MS, and time splitting-TS). With the objective of maximizing the minimum user rate, we then propose a unified successive convex approximation (SCA)-based alternative optimization (AO) algorithm to jointly optimize the transmit active beamforming, common rate allocation, STAR RIS passive beamforming, as well as time allocation (for HD or TS protocols) subject to the transmit power constraint at the base station (BS) and the law of energy conservation at the STAR RIS. To alleviate the computational burden, we further propose a low-complexity algorithm that incorporates a closed-form passive beamforming design. Numerical results show that our proposed framework significantly enhances user fairness compared with conventional CRS schemes without STAR RIS or other STAR RIS empowered multiple access schemes. Moreover, the proposed low-complexity algorithm dramatically reduces the computational complexity while achieving very close performance to the AO method.

In this work, we study the out-of-distribution (OOD) detection problem through the use of the feature space of a pre-trained deep classifier. We show that learning the density of in-distribution (ID) features with an energy-based models (EBM) leads to competitive detection results. However, we found that the non-mixing of MCMC sampling during the EBM's training undermines its detection performance. To overcome this an energy-based correction of a mixture of class-conditional Gaussian distributions. We obtains favorable results when compared to a strong baseline like the KNN detector on the CIFAR-10/CIFAR-100 OOD detection benchmarks.

In this work, we consider the problem of localizing multiple signal sources based on time-difference of arrival (TDOA) measurements. In the blind setting, in which the source signals are not known, the localization task is challenging due to the data association problem. That is, it is not known which of the TDOA measurements correspond to the same source. Herein, we propose to perform joint localization and data association by means of an optimal transport formulation. The method operates by finding optimal groupings of TDOA measurements and associating these with candidate source locations. To allow for computationally feasible localization in three-dimensional space, an efficient set of candidate locations is constructed using a minimal multilateration solver based on minimal sets of receiver pairs. In numerical simulations, we demonstrate that the proposed method is robust both to measurement noise and TDOA detection errors. Furthermore, it is shown that the data association provided by the proposed method allows for statistically efficient estimates of the source locations.

In this work, we propose fully nonconforming, locally exactly divergence-free discretizations based on lowest order Crouziex-Raviart finite element and piecewise constant spaces to study the optimal control of stationary double diffusion model presented in [B\"urger, M\'endez, Ruiz-Baier, SINUM (2019), 57:1318-1343]. The well-posedness of the discrete uncontrolled state and adjoint equations are discussed using discrete lifting and fixed point arguments, and convergence results are derived rigorously under minimal regularity. Building upon our recent work [Tushar, Khan, Mohan arXiv (2023)], we prove the local optimality of a reference control using second-order sufficient optimality condition for the control problem, and use it along with an optimize-then-discretize approach to prove optimal order a priori error estimates for the control, state and adjoint variables upto the regularity of the solution. The optimal control is computed using a primal-dual active set strategy as a semi-smooth Newton method and computational tests validate the predicted error decay rates and illustrate the proposed scheme's applicability to optimal control of thermohaline circulation problems.