Theoretical Upperbound Research Articles

Optimised GRS coded cooperation: sliding relay selection design and improved joint decoding

ABSTRACT In this paper, the novel optimised generalised Reed-Solomon coded cooperative (OGRSCC) scheme is developed with a flexible selection of the code length and information dimension. In the OGRSCC scheme, two GRS codes with different dimensions are deployed at the source and relay, respectively, where the information symbols of the relay are dependent on those of the source. At the relay, different symbol selections may contribute to distinct joint codes at the destination. As a result, to achieve a maximum free distance (FD) and the optimised weight distribution of the final code, the global search method is first proposed to obtain the optimal selection pattern. However, as the code grows longer, its complexity rises dramatically. To make the selection more practical, the low-complexity sliding search method is then investigated to obtain the local optimal symbol selection pattern. Monte-Carlo simulated results indicate the OGRSCC scheme with two selection methods demonstrates almost identical performance. Furthermore, based on this special selection method and the unique algebraic structure of GRS code, the improved joint decoding algorithm is first proposed to boost the overall system performance. In addition, the theoretical upper bound is analysed, verifying the effectiveness of the proposed OGRSCC scheme. Numerical simulations reveal that the proposed OGRSCC scheme outperforms its corresponding non-cooperative scheme by a gain of over 3.2 dB and its existing comparable schemes by a margin of approximately more than 4 dB at high signal-to-noise ratio (SNR), respectively.

Super-Oscillating Diffractive Optical Spot Generators

The prior discrete Fourier transform (PDFT) is applied to the design of super-oscillating diffractive optical elements with rotational symmetry. Numerical simulations of the filter response are used to demonstrate the potential of the PDFT-based approach, which includes a regularization method for improved numerical and functional stability of the filter design. For coherent monochromatic illumination, the Strehl ratio of spot generators as a function of the spot radius is compared to the theoretical upper bound. It is shown that the performance of the PDFT design varies significantly depending on the aperture function and the encoding as a phase-only diffractive element. Experimental results are in good agreement with simulations and demonstrate the moderate demands to implement super-oscillating diffractive optical elements.

Eigenvalue-based quantum state verification of three-qubit W class states

In quantum many-body systems, W class states are typical examples of states with genuine multipartite entanglement. They have been found to be valuable resources in many quantum information processing tasks. However, the characterization and verification of W class states still remains an intractable problem. Here we first propose an eigenvalue-based verification protocol consisting of four practical adaptive local projective measurement tests, and obtain the optimal test probabilities with particle swarm optimization algorithm. The efficiency achieved by this protocol is far from satisfactory when compared with the theoretical upper bound. Then by utilizing the symmetry of the target states and a class of specific unitaries, we optimize the original verification strategy based on group theory. In this case, our new protocol can realize the efficient verification of three-qubit W class states.

Segment Anything Model Can Not Segment Anything: Assessing AI Foundation Model’s Generalizability in Permafrost Mapping

This paper assesses trending AI foundation models, especially emerging computer vision foundation models and their performance in natural landscape feature segmentation. While the term foundation model has quickly garnered interest from the geospatial domain, its definition remains vague. Hence, this paper will first introduce AI foundation models and their defining characteristics. Built upon the tremendous success achieved by Large Language Models (LLMs) as the foundation models for language tasks, this paper discusses the challenges of building foundation models for geospatial artificial intelligence (GeoAI) vision tasks. To evaluate the performance of large AI vision models, especially Meta’s Segment Anything Model (SAM), we implemented different instance segmentation pipelines that minimize the changes to SAM to leverage its power as a foundation model. A series of prompt strategies were developed to test SAM’s performance regarding its theoretical upper bound of predictive accuracy, zero-shot performance, and domain adaptability through fine-tuning. The analysis used two permafrost feature datasets, ice-wedge polygons and retrogressive thaw slumps because (1) these landform features are more challenging to segment than man-made features due to their complicated formation mechanisms, diverse forms, and vague boundaries; (2) their presence and changes are important indicators for Arctic warming and climate change. The results show that although promising, SAM still has room for improvement to support AI-augmented terrain mapping. The spatial and domain generalizability of this finding is further validated using a more general dataset EuroCrops for agricultural field mapping. Finally, we discuss future research directions that strengthen SAM’s applicability in challenging geospatial domains.

Adjoint method in machine learning: A pathway to efficient inverse design of photonic devices

Innovative machine learning techniques have facilitated the inverse design of photonic structures for numerous practical applications. Nevertheless, the quantity of data and the initial data distribution are paramount for the discovery of highly efficient photonic devices. These devices often require simulated data ranging from thousands to several hundred thousand data points. This issue has consistently posed a major hurdle in machine learning-based photonic design problems. Therefore, we propose a new data augmentation algorithm grounded in the adjoint method, capable of generating more than 300 times the amount of original data while enhancing device efficiency. The adjoint method forecasts changes in the figure of merit (FoM) resulting from structural perturbations, requiring only two full-wave Maxwell simulations for this prediction. By leveraging the adjoint gradient values, we can augment and label several thousand new data points without any additional computations. Furthermore, the augmented data generated by the proposed algorithm displays significantly improved FoMs. We apply this algorithm to a multi-layered metalens design problem and demonstrate that it consequently exhibits a 343-fold increase in data generation efficiency. After incorporating the proposed algorithm into a generative adversarial network, the optimized metalens exhibits a maximum focusing efficiency of 92.93%, comparable to the theoretical upper bound.

Lifelong learning with deep conditional generative replay for dynamic and adaptive modeling towards net zero emissions target in building energy system

Deep learning has been advocated as the predominant modeling method in the next-generation green building energy systems for energy prediction, predictive maintenance and control optimization. However, in response to external changes, the limited adaptability to new contents and catastrophic forgetting of previously learnt knowledge result in diminished accuracy and robustness, significantly blocking its practical application. To this end, a novel lifelong learning method with deep generative replay was proposed for dynamic and adaptive modeling to conserve energy and mitigate emissions in building energy systems. The presented lifelong learning method was characterized by the alternate training of the task solver and the replay generator in sequential energy task learning to alleviate the catastrophic forgetting. The replay generator provided the past data for the task solver to retain previous energy knowledge while learn new information, which was a conditional generative model instead of explicitly storing data to save resources and protect privacy. In order to validate its technical feasibility, a field experiment was conducted in a specially constructed net zero energy building for the case study on solar power generation prediction. The overall accuracy of proposed method was 53.4% higher than the standard method through fine-tuning and reached 0.89, which closely approaches the theoretical upper bound of 0.91 obtained by the joint training. Moreover, the proposed method effectively retained previously learnt knowledge in sequential energy task learning, evidenced by an average forgetting rate lower than 0.10. Furthermore, extensive comparative experiments have demonstrated the superiority of the proposed method over other machine learning models based on retraining or incremental training. Our study is expected to develop more flexible and robust deep learning models for improving energy efficiency and promoting the carbon neutrality in building energy systems.

Improved Linear Decomposition of Majority and Threshold Boolean Functions

To support efficient design automation for emerging computing fabrics, novel data structures for logic synthesis and technology mapping are being intensively studied. It has been shown that for several promising computing technologies intermediate forms like Majority-Inverter Graph (MIG), and Xor-Majority Graph (XMG) can be particularly beneficial. This has propelled the Boolean majority operator at the forefront of research. Though these structures primarily utilise 3-input Majority nodes, the efficacy of n-input Majority operators has been demonstrated as well. A long-standing research problem, in that context and also for theoretical circuit complexity, is to determine efficient decomposition of an n-input Majority (Majn) function in terms of 3-input Majority (Maj3) operator. In this manuscript, we make two significant advances in this topic. First, a practically realizable linear decomposition is provided, thus improving the previously reported quadratic bounds. Second, the theoretical upper bound of decomposing Majn, in terms of Maj3, is reduced from 5.884n to 3n. The erstwhile theoretical upper bound of 5.884n also lacked a practical construction for Majn decomposition, presumably due to the presence of sequential elements in the algorithm. The proof of the linearity, detailed construction procedure along with experimental studies using state-of-the-art synthesis flows to validate the aforementioned claims are presented in this work. The results are applicable to threshold Boolean functions, too.

A global 5 km monthly potential evapotranspiration dataset (1982–2015) estimated by the Shuttleworth–Wallace model

Abstract. As the theoretical upper bound of evapotranspiration (ET) or water use by ecosystems, potential ET (PET) has always been widely used as a variable linking a variety of disciplines, such as climatology, ecology, hydrology, and agronomy. However, substantial uncertainties exist in the current PET methods (e.g., empiric models and single-layer models) and datasets because of unrealistic configurations of land surface and unreasonable parameterizations. Therefore, this study comprehensively considered interspecific differences in various vegetation-related parameters (e.g., plant stomatal resistance and CO2 effects on stomatal resistance) to calibrate and parametrize the Shuttleworth–Wallace (SW) model for forests, shrubland, grassland, and cropland. We derived the parameters using identified daily ET observations with no water stress (i.e., PET) at 96 eddy covariance (EC) sites across the globe. Model validations suggest that the calibrated model could be transferable from known observations to any location. Based on four popular meteorological datasets, relatively realistic canopy height, time-varying land use or land cover, and the leaf area index, we generated a global 5 km ensemble mean monthly PET dataset that includes two components of potential transpiration (PT) and soil evaporation (PE) for the 1982–2015 time period. Using this new dataset, the climatological characteristics of PET partitioning and the spatiotemporal changes in PET, PE, and PT were investigated. The global mean annual PET was 1198.96 mm with PT/PET of 41 % and PE/PET of 59 %, controlled moreover by PT and PE of over 41 % and 59 % of the globe, respectively. Globally, the annual PET and PT significantly (p<0.05) increase by 1.26 and 1.27 mm yr−1 over the last 34 years, followed by a slight decrease in the annual PE. Overall, the annual PET changes over 53 % of the globe could be attributed to PT, and the rest to PE. The new PET dataset may be used by academic communities and various agencies to conduct climatological analyses, hydrological modeling, drought studies, agricultural water management, and biodiversity conservation. The dataset is available at https://doi.org/10.11888/Terre.tpdc.300193 (Sun et al., 2023).

Unawareness detection: Discovering black-box malicious models and quantifying privacy leakage risks

Because machine learning models, especially black-box malicious models vulnerable to attribute inference attacks, are capable of generating a great deal of privacy leakage, recent work has focused on assessing these models in an attempt to prevent unexpected attribute privacy leakage. While there has been some success at model privacy risk evaluations, these traditional solutions are almost brittle in practice because they not only require white-box access to obtain model feature layer outputs but also their evaluation results are heavily influenced by the training dataset and the model structure, leading to difficulty in generalization. In this paper, we propose a novel unawareness detection mechanism for discovering black-box malicious models and quantifying potential unawareness privacy leakage risk along with machine learning models to overcome the two limitations. A new method for quantifying the privacy risk caused by a specific loss function has been proposed to mitigate the impact of the training dataset and the model structure. A new evaluation model has also been proposed that uses Matthew's correlation coefficient score as a new metric and the final output of the target model as a new input. In addition, the theoretical upper bound of the model privacy risk has also been given a mathematical formula that is positively correlated to the mutual information between the sensitive attributes and the target model outputs. Compared with traditional detection methods, our evaluation model reduces the requirement for model access and minimizes evaluation errors caused by data imbalance, and our privacy risk assessment method and theoretical upper bounds on privacy risk can be applied to a broader range of datasets and target model structures. The experimental results show that the adversary's prediction capability is affected by the distribution of datasets and the level of malicious intent of the model, which is consistent with the theoretical prediction, and the detecting method can find potential model privacy leaks in public datasets UTKFace and FairFace.

A method to improve the update rate of underwater acoustic positioning system

Underwater positioning system obtains relative position between a transponder and a transceiver by measuring round trip time (RTT) and angle of arrival. The position update rate (PUR) cannot be greater than 1/RTT, and when one transceiver locates multiple transponders, the PUR becomes smaller. This paper proposes a method to increase the PUR. The proposed method minimizes “idle time” by allowing the transceiver to send additional pings without packet transmission-reception collisions, rather than waiting for the response to the previous ping sent to the transponder. It is essential that the reception (transmission) of the ping and the transmission (reception) of the response should not be overlapped in the transponder (transceiver). In order to avoid these collisions, the ping transmission time is adaptively determined by considering the bound of packet reception times drawn by ping duration (PD), response signal duration (RD), and the maximum relative speed. In addition, the transceiver assigns a delay before sending the response signal upon receiving each ping. These adaptive features effectively adapt to changes due to mobility. We derive a theoretical upper bound of the PUR and verify this bound by computer simulations. [Work supported by KIMST funded by the Agency of Korea Coast Guard (KIMST-20210547).]

End-to-end DVB-S2X system design with DL-based channel estimation over satellite fading channels at Ka-band

Satellite channels suffer from heavy fading due to the atmospheric impairments at high frequencies. Therefore, channel estimation is essential for coherent detection and demodulation in satellite-coded systems. The conventional minimum mean square error (MMSE) estimator (the theoretical upper bound) requires a priori knowledge about the channel statistics which is not feasible to obtain in a real transmission. Also, it suffers from high complexity. However, deep learning (DL) estimators do not require any information about the channel statistics. Therefore, in this paper, two DL-based channel estimators are proposed for digital and video broadcasting second generation extension (DVB-S2X) system with less complexity than the MMSE estimator. In particular, the bidirectional long-short term memory (BLSTM) and the gated recurrent unit (GRU) are adopted in our proposed estimators which are termed as DLBLSTM and DLGRU, respectively. The proposed estimators evaluated over two satellite fading channels; one with heavy fading and the other with low fading. Moreover, these estimators are compared with the conventional estimators, the least square (LS) and the MMSE, in terms of the normalized mean square error (NMSE) and the bit error rate (BER). Simulation results show that the proposed DL-based estimators have better performance than the LS estimator and the DLBLSTM has better performance than the DLGRU estimator in terms of NMSE and BER with both satellite channels.

FlexBlock: A Flexible DNN Training Accelerator With Multi-Mode Block Floating Point Support

When training deep neural networks (DNNs), expensive floating point arithmetic units are used in GPUs or custom neural processing units (NPUs). To reduce the burden of floating point arithmetic, community has started exploring the use of more efficient data representations, e.g., block floating point (BFP). The BFP format allows a group of values to share an exponent, which effectively reduces the memory footprint and enables cheaper fixed point arithmetic for multiply-accumulate (MAC) operations. However, existing BFP-based DNN accelerators are targeted for a specific precision, making them less versatile. In this paper, we present FlexBlock, a DNN training accelerator with three BFP modes, possibly different among activation, weight, and gradient tensors. By configuring FlexBlock to a lower BFP precision, the number of MACs handled by the core increases by up to 4× in 8-bit mode or 16× in 4-bit mode compared to 16-bit mode. To reach this theoretical upper bound, FlexBlock maximizes the core utilization at various precision levels or layer types, and allows dynamic precision control to keep throughput at its peak without sacrificing training accuracy. We evaluate the effectiveness of FlexBlock using representative DNNs on CIFAR, ImageNet and WMT14 datasets. As a result, training in FlexBlock significantly improves training speed by 1.5 5.3× and energy efficiency by 2.4 7.0× compared to other training accelerators.

DropMessage: Unifying Random Dropping for Graph Neural Networks

Graph Neural Networks (GNNs) are powerful tools for graph representation learning. Despite their rapid development, GNNs also face some challenges, such as over-fitting, over-smoothing, and non-robustness. Previous works indicate that these problems can be alleviated by random dropping methods, which integrate augmented data into models by randomly masking parts of the input. However, some open problems of random dropping on GNNs remain to be solved. First, it is challenging to find a universal method that are suitable for all cases considering the divergence of different datasets and models. Second, augmented data introduced to GNNs causes the incomplete coverage of parameters and unstable training process. Third, there is no theoretical analysis on the effectiveness of random dropping methods on GNNs. In this paper, we propose a novel random dropping method called DropMessage, which performs dropping operations directly on the propagated messages during the message-passing process. More importantly, we find that DropMessage provides a unified framework for most existing random dropping methods, based on which we give theoretical analysis of their effectiveness. Furthermore, we elaborate the superiority of DropMessage: it stabilizes the training process by reducing sample variance; it keeps information diversity from the perspective of information theory, enabling it become a theoretical upper bound of other methods. To evaluate our proposed method, we conduct experiments that aims for multiple tasks on five public datasets and two industrial datasets with various backbone models. The experimental results show that DropMessage has the advantages of both effectiveness and generalization, and can significantly alleviate the problems mentioned above. A detailed version with full appendix can be found on arXiv: https://arxiv.org/abs/2204.10037.

Super-resolution model-based iterative reconstruction for lens-coupled micro-CT imaging

Lens-coupled high-resolution micro-computed tomography (micro-CT) uses a visible light magnification system behind the x-ray path to achieve higher resolution imaging than conventional micro-CT. However, the spatial resolution is theoretically limited by optical diffraction and mechanical control precision. As a result, the current system resolution is still insufficient for some applications, such as the imaging of biological materials whose structures are on the nanometer scale. To overcome this limitation, a super-resolution algorithm can be employed to improve the image resolution beyond the theoretical upper bound of the ideal spatial resolution of the system. In this work, a super-resolution model-based iterative reconstruction (SR-MBIR) algorithm is proposed based on a lens-coupled high-resolution micro-CT system and a high-precision nano-stage attached to the rotation stage of the system. The algorithm employs a scanning program that dithers the object via the nano-stage to obtain multiple sets of projection images with sub-pixel information. The blur and noise statistical models are introduced into the physical model for iterative reconstruction, allowing for super-resolution, deblurring, and noise suppression. The results of simulation data and actual data show that the SR-MBIR algorithm has a prominent effect in improving image resolution. The reconstructed images have sharper edges, better details, higher signal-to-noise ratio, and can effectively suppress the systematic blur and noise in the imaging process, thus achieving superior interior reconstruction quality.

Theoretical upper bound of multiplexing in biological sensory receptors

Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.

An Intelligent Framework for Oversubscription Management in CPU-GPU Unified Memory

This paper proposes a novel intelligent framework for oversubscription management in CPU-GPU UVM. We analyze the current rule-based methods of GPU memory oversubscription with unified memory, and the current learning-based methods for other computer architectural components. We then identify the performance gap between the existing rule-based methods and the theoretical upper bound. We also identify the advantages of applying machine intelligence and the limitations of the existing learning-based methods. This paper proposes a novel intelligent framework for oversubscription management in CPU-GPU UVM. It consists of an access pattern classifier followed by a pattern-specific Transformer-based model using a novel loss function aiming for reducing page thrashing. A policy engine is designed to leverage the model's result to perform accurate page prefetching and pre-eviction. We evaluate our intelligent framework on a set of 11 memory-intensive benchmarks from popular benchmark suites. Our solution outperforms the state-of-the-art (SOTA) methods for oversubscription management, reducing the number of pages thrashed by 64.4\% under 125\% memory oversubscription compared to the baseline, while the SOTA method reduces the number of pages thrashed by 17.3\%. Our solution achieves an average IPC improvement of 1.52X under 125\% memory oversubscription, and our solution achieves an average IPC improvement of 3.66X under 150\% memory oversubscription. Our solution outperforms the existing learning-based methods for page address prediction, improving top-1 accuracy by 6.45\% (up to 41.2\%) on average for a single GPGPU workload, improving top-1 accuracy by 10.2\% (up to 30.2\%) on average for multiple concurrent GPGPU workloads.

Limiting Performance of the Ejector Refrigeration Cycle with Pure Working Fluids

An ejector refrigeration system is a promising heat-driven refrigeration technology for energy consumption. The ideal cycle of an ejector refrigeration cycle (ERC) is a compound cycle with an inverse Carnot cycle driven by a Carnot cycle. The coefficient of performance (COP) of this ideal cycle represents the theoretical upper bound of ERC, and it does not contain any information about the properties of working fluids, which is a key cause of the large energy efficiency gap between the actual cycle and the ideal cycle. In this paper, the limiting COP and thermodynamics perfection of subcritical ERC is derived to evaluate the ERC efficiency limit under the constraint of pure working fluids. 15 pure fluids are employed to demonstrate the effects of working fluids on limiting COP and limiting thermodynamics perfection. The limiting COP is expressed as the function of the working fluid thermophysical parameters and the operating temperatures. The thermophysical parameters are the specific entropy increase in the generating process and the slope of the saturated liquid, and the limiting COP increases with these two parameters. The result shows R152a, R141b, and R123 have the best performance, and the limiting thermodynamic perfections at the referenced state are 86.8%, 84.90%, and 83.67%, respectively.

North Atlantic Tropical Cyclone Outer Size and Structure Remain Unchanged by the Late Twenty-First Century

Abstract There is a lack of consensus on whether North Atlantic tropical cyclone (TC) outer size and structure (i.e., change in outer winds with increasing radius from the TC) will differ by the late twenty-first century. Hence, this work seeks to examine whether North Atlantic TC outer wind field size and structure will change by the late twenty-first century using multiple simulations under CMIP3 SRES A1B and CMIP5 RCP4.5 scenarios. Specifically, our analysis examines data from the GFDL High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR) and two versions of the GFDL hurricane model downscaling climate model output. Our results show that projected North Atlantic TC outer size and structure remain unchanged by the late twenty-first century within nearly all HiFLOR and GFDL hurricane model simulations. Moreover, no significant regional outer size differences exist in the North Atlantic within most HiFLOR and GFDL hurricane model simulations. No changes between the control and late-twenty-first-century simulations exist over the storm life cycle in nearly all simulations. For the simulation that shows significant decreases in TC outer size, the changes are attributed to reductions in storm lifetime and outer size growth rates. The absence of differences in outer size among most simulations is consistent with the process that controls the theoretical upper bound of storm size (i.e., Rhines scaling), which is thermodynamically invariant. However, the lack of complete consensus among simulations for many of these conclusions suggests nontrivial uncertainty in our results.

On energy dissipation or harvesting of tuned viscous mass dampers for SDOF structures under seismic excitations

In the past decade, tuned viscous mass dampers (TVMD) have been demonstrated as effective seismic resistant dampers. However, theoretical study on energy dissipation or energy harvesting of the TVMD has rarely been investigated, particularly, whether or not its optimal passive vibration control and energy dissipation maximization are consistent remains questionable. Here, from the theoretical perspective, we present an analysis of energy dissipation or energy harvesting of the TVMD in terms of damping power or output power, respectively. We derive the closed-form solutions of the average damping power of a single-degree-of-freedom (SDOF) structure-TVMD system under white-noise base excitations or seismic excitations modeled by the Kanai-Tajimi spectra, which is verified against the Monte Carlo simulations. Based on the closed-form solutions, the influences of the TVMD parameters, site conditions, and structural dynamic characteristics on the average damping power are analyzed via a parametric study. Theoretical results indicate that structural damping, site condition, structural period, frequency ratio, and inertance-to-mass ratio have a significant impact on the damping power or dissipated energy. In addition, the TVMD dissipates much more energy at a soft-soil site than at a stiff-soil site. At a stiff-soil site, the TVMD dissipates more energy for a short-period structure than for a long-period structure, however, at a soft-soil site, the law is the opposite. The study also presents the theoretical upper bound of the output power of an energy-harvesting TVMD. Particularly, results also illustrate that the maximization of TVMD energy dissipation is not consistent with the optimal passive vibration control. This study may shed light on the TVMD studies for seismic response control or energy harvesting purposes in the years to come.

Guaranteed Privacy of Distributed Nonconvex Optimization via Mixed-Monotone Functional Perturbations

In this letter, we introduce a new notion of guaranteed privacy for distributed nonconvex optimization algorithms. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism which is based on deterministic, but unknown affine perturbations of the local objective functions. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. This is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is independent of the chosen optimization algorithm. Finally, simulation results illustrate the accuracy-privacy trade-off and that our approach outperforms a benchmark differentially private distributed optimization algorithm in the literature.