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Randomized smoothing has emerged as a potent certifiable defense against adversarial attacks by employing smoothing noises from specific distributions to ensure the robustness of a smoothed classifier. However, the utilization of Monte Carlo sampling in this process introduces a compute-intensive element, which constrains the practicality of randomized smoothing on a larger scale. To address this limitation, we propose a novel approach that replaces Monte Carlo sampling with the training of a surrogate neural network. Through extensive experimentation in various settings, we demonstrate the efficacy of our approach in approximating the smoothed classifier with remarkable precision. Furthermore, we demonstrate that our approach significantly accelerates the robust radius certification process, providing nearly $600$X improvement in computation time, overcoming the computational bottlenecks associated with traditional randomized smoothing.

Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defence mechanisms often fall short, as new attacks constantly emerge, rendering existing defences obsolete. A paradigm shift from empirical defences to certification-based defences has been observed in response. Randomized smoothing has emerged as a promising technique among notable advancements. This study reviews the theoretical foundations, empirical effectiveness, and applications of randomized smoothing in verifying machine learning classifiers. We provide an in-depth exploration of the fundamental concepts underlying randomized smoothing, highlighting its theoretical guarantees in certifying robustness against adversarial perturbations. Additionally, we discuss the challenges of existing methodologies and offer insightful perspectives on potential solutions. This paper is novel in its attempt to systemise the existing knowledge in the context of randomized smoothing.

While the use of artificial intelligence (AI) for medical image analysis is gaining wide acceptance, the expertise, time and cost required to generate annotated data in the medical field are significantly high, due to limited availability of both data and expert annotation. Strongly supervised object localization models require data that is exhaustively annotated, meaning all objects of interest in an image are identified. This is difficult to achieve and verify for medical images. We present a method for the transformation of real data to train any Deep Neural Network to solve the above problems. We show the efficacy of this approach on both a weakly supervised localization model and a strongly supervised localization model. For the weakly supervised model, we show that the localization accuracy increases significantly using the generated data. For the strongly supervised model, this approach overcomes the need for exhaustive annotation on real images. In the latter model, we show that the accuracy, when trained with generated images, closely parallels the accuracy when trained with exhaustively annotated real images. The results are demonstrated on images of human urine samples obtained using microscopy., Comment: https://openaccess.thecvf.com/content_CVPRW_2020/html/w57/Kushwaha_Rapid_Training_Data_Creation_by_Synthesizing_Medical_Images_for_Classification_CVPRW_2020_paper.html

This paper is a contribution to the reproducibility challenge in the field of machine learning, specifically addressing the issue of certifying the robustness of neural networks (NNs) against adversarial perturbations. The proposed Double Sampling Randomized Smoothing (DSRS) framework overcomes the limitations of existing methods by using an additional smoothing distribution to improve the robustness certification. The paper provides a clear manifestation of DSRS for a generalized family of Gaussian smoothing and a computationally efficient method for implementation. The experiments on MNIST and CIFAR-10 demonstrate the effectiveness of DSRS, consistently certifying larger robust radii compared to other methods. Also various ablations studies are conducted to further analyze the hyperparameters and effect of adversarial training methods on the certified radius by the proposed framework.

Deciding setpoints for distributed energy resources (DERs) via local control rules rather than centralized optimization offers significant autonomy. The IEEE Standard 1547 recommends deciding DER setpoints using Volt/VAR rules. Although such rules are specified as non-increasing piecewise-affine, their exact shape is left for the utility operators to decide and possibly customize per bus and grid conditions. To address this need, this work optimally designs Volt/VAR rules to minimize ohmic losses on lines while maintaining voltages within allowable limits. This is practically relevant as excessive reactive injections could reduce equipment's lifetime due to overloading. We consider a linearized single-phase grid model. Even under this setting, optimal rule design (ORD) is technically challenging as Volt/VAR rules entail mixed-integer models, stability implications, and uncertainties in grid loading. Uncertainty is handled by minimizing the average losses under voltage chance constraints. To cope with the piecewise-affine shape of the rules, we build upon our previous reformulation of ORD as a deep learning task. A recursive neural network (RNN) surrogates Volt/VAR dynamics and thanks to back-propagation, we expedite this chance-constrained ORD. RNN weights coincide with rule parameters, and are trained using primal-dual decomposition. Numerical tests corroborate the efficacy of this novel ORD formulation and solution methodology.

How genes affect tissue scale organization remains a longstanding biological puzzle. As experimental efforts are underway to solve this puzzle via quantification of gene expression and sub-cellular, cellular and tissue structure, computational efforts remain far behind. To potentially help accelerate the computational efforts, we review two recent publications, the first on a cellular-based model for tissues and the second on a cell nucleus model consisting of chromatin and a lamina shell. We then give a perspective on how the two models can be combined to test multiscale hypotheses linking the chromatin scale and the tissue scale. To be concrete, we turn to an in vitro system for the brain known as a brain organoid. We provide a multiscale hypothesis to distinguish structural differences between brain organoids built from induced-pluripotent human stem cells and from induced-pluripotent gorilla and chimpanzee stem cells. Recent experiments discover that a cell fate transition from neuroepithelial cells to radial glial cells includes a new intermediate state that is delayed in human-derived brain organoids as compared to their genetically-close relatives, which significantly narrows and lengthens the cells on the apical side [1]. Additional experiments revealed that the protein ZEB2 plays a major role in the emergence of this new intermediate state with ZEB2 mRNA levels peaking at the onset of the emergence [1]. We postulate that the enhancement of ZEB2 expression driving this intermediate state is potentially due to chromatin reorganization. More precisely, there exists critical strain triggering the reorganization that is higher for human-derived stem cells, thereby resulting in a delay. Such a hypothesis can readily be tested experimentally within individual cells and within brain organoids as well as computationally to work towards solving the gene-to-tissue organization puzzle., Comment: 13 pages, 8 figures

Nanoparticles, such as viruses, can enter cells via endocytosis. During endocytosis, the cell surface wraps around the nanoparticle to effectively eat it. Prior focus has been on how nanoparticle size and shape impacts endocytosis. However, inspired by the noted presence of extracellular vimentin affecting viral and bacteria uptake, as well as the structure of coronaviruses, we construct a computational model in which both the cell-like construct and the virus-like construct contain filamentous protein structures protruding from their surfaces. We then study the impact of these additional degrees of freedom on viral wrapping. We find that cells with an optimal density of filamentous extracellular components (ECCs) are more likely to be infected as they uptake the virus faster and use relatively less cell surface area per individual virus. At the optimal density, the cell surface folds around the virus, and folds are faster and more efficient at wrapping the virus than crumple-like wrapping. We also find that cell surface bending rigidity helps generate folds, as bending rigidity enhances force transmission across the surface. However, changing other mechanical parameters, such as the stretching stiffness of filamentous ECCs or virus spikes, can drive crumple-like formation of the cell surface. We conclude with the implications of our study on the evolutionary pressures of virus-like particles, with a particular focus on the cellular microenvironment that may include filamentous ECCs., Comment: 15 pages, 8 figures

Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) have been shown numerically to generate high-quality solutions to hard combinatorial problems, yet incorporating constraints to such problems has been elusive. To this end, this work puts forth a quantum heuristic to cope with stochastic binary quadratically constrained quadratic programs (QCQP). Identifying the strength of quantum circuits to efficiently generate samples from probability distributions that are otherwise hard to sample from, the variational quantum circuit is trained to generate binary-valued vectors to approximately solve the aforesaid stochastic program. The method builds upon dual decomposition and entails solving a sequence of judiciously modified standard VQE tasks. Tests on several synthetic problem instances using a quantum simulator corroborate the near-optimality and feasibility of the method, and its potential to generate feasible solutions for the deterministic QCQP too.

Volt/VAR control rules facilitate the autonomous operation of distributed energy resources (DER) to regulate voltage in power distribution grids. According to non-incremental control rules, such as the one mandated by the IEEE Standard 1547, the reactive power setpoint of each DER is computed as a piecewise-linear curve of the local voltage. However, the slopes of such curves are upper-bounded to ensure stability. On the other hand, incremental rules add a memory term into the setpoint update, rendering them universally stable. They can thus attain enhanced steady-state voltage profiles. Optimal rule design (ORD) for incremental rules can be formulated as a bilevel program. We put forth a scalable solution by reformulating ORD as training a deep neural network (DNN). This DNN emulates the Volt/VAR dynamics for incremental rules derived as iterations of proximal gradient descent (PGD). Analytical findings and numerical tests corroborate that the proposed ORD solution can be neatly adapted to single/multi-phase feeders.

Distribution grids are challenged by rapid voltage fluctuations induced by variable power injections from distributed energy resources (DERs). To regulate voltage, the IEEE Standard 1547 recommends each DER inject reactive power according to piecewise-affine Volt/VAR control rules. Although the standard suggests a default shape, the rule can be customized per bus. This task of optimal rule design (ORD) is challenging as Volt/VAR rules introduce nonlinear dynamics, and lurk trade-offs between stability and steady-state voltage profiles. ORD is formulated as a mixed-integer nonlinear program (MINLP), but scales unfavorably with the problem size. Towards a more efficient solution, we reformulate ORD as a deep learning problem. The idea is to design a DNN that emulates Volt/VAR dynamics. The DNN takes grid scenarios as inputs, rule parameters as weights, and outputs equilibrium voltages. Optimal rule parameters can be found by training the DNN so its output approaches unity for various scenarios. The DNN is only used to optimize rules and is never employed in the field. While dealing with ORD, we also review and expand on stability conditions and convergence rates for Volt/VAR dynamics on single- and multi-phase feeders. Tests showcase the merit of DNN-based ORD by benchmarking it against its MINLP counterpart., Comment: Accepted in the IEEE Trans. on Smart Grid

The IEEE 1547 Standard for the interconnection of distributed energy resources (DERs) to distribution grids provisions that smart inverters could be implementing Volt/VAR control rules among other options. Such rules enable DERs to respond autonomously in response to time-varying grid loading conditions. The rules comprise affine droop control augmented with a deadband and saturation regions. Nonetheless, selecting the shape of these rules is not an obvious task, and the default options may not be optimal or dynamically stable. To this end, this work develops a novel methodology for customizing Volt/VAR rules on a per-bus basis for a single-phase feeder. The rules are adjusted by the utility every few hours depending on anticipated demand and solar scenarios. Using a projected gradient descent-based algorithm, rules are designed to improve the feeder's voltage profile, comply with IEEE 1547 constraints, and guarantee stability of the underlying nonlinear grid dynamics. The stability region is inner approximated by a polytope and the rules are judiciously parameterized so their feasible set is convex. Numerical tests using real-world data on the IEEE 141-bus feeder corroborate the scalability of the methodology and its explore the trade-offs of Volt/VAR control with alternatives.

Representing 3D objects and scenes with neural radiance fields has become very popular over the last years. Recently, surface-based representations have been proposed, that allow to reconstruct 3D objects from simple photographs. However, most current techniques require an accurate camera calibration, i.e. camera parameters corresponding to each image, which is often a difficult task to do in real-life situations. To this end, we propose a method for learning 3D surfaces from noisy camera parameters. We show that we can learn camera parameters together with learning the surface representation, and demonstrate good quality 3D surface reconstruction even with noisy camera observations., Comment: 4 pages - 2 for paper, 2 for supplementary

This effort aims to reproduce the results of experiments and analyze the robustness of the review framework for knowledge distillation introduced in the CVPR '21 paper 'Distilling Knowledge via Knowledge Review' by Chen et al. Previous works in knowledge distillation only studied connections paths between the same levels of the student and the teacher, and cross-level connection paths had not been considered. Chen et al. propose a new residual learning framework to train a single student layer using multiple teacher layers. They also design a novel fusion module to condense feature maps across levels and a loss function to compare feature information stored across different levels to improve performance. In this work, we consistently verify the improvements in test accuracy across student models as reported in the original paper and study the effectiveness of the novel modules introduced by conducting ablation studies and new experiments., Comment: This is a reproducibility effort based on the CVPR '21 paper 'Distilling Knowledge via Knowledge Review' by Chen et al

A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF formulations consider simple control policies such as affine policies that are mathematically simple and resemble many policies used in current practice. Motivated by the efficacy of machine learning (ML) algorithms and the potential benefits of general control policies for cost and constraint enforcement, we put forth a deep neural network (DNN)-based policy that predicts the generator dispatch decisions in real time in response to uncertainty. The weights of the DNN are learnt using stochastic primal-dual updates that solve the SOPF without the need for prior generation of training labels and can explicitly account for the feasibility constraints in the SOPF. The advantages of the DNN policy over simpler policies and their efficacy in enforcing safety limits and producing near optimal solutions are demonstrated in the context of a chance constrained formulation on a number of test cases.

Coordinating inverters at scale under uncertainty is the desideratum for integrating renewables in distribution grids. Unless load demands and solar generation are telemetered frequently, controlling inverters given approximate grid conditions or proxies thereof becomes a key specification. Although deep neural networks (DNNs) can learn optimal inverter schedules, guaranteeing feasibility is largely elusive. Rather than training DNNs to imitate already computed optimal power flow (OPF) solutions, this work integrates DNN-based inverter policies into the OPF. The proposed DNNs are trained through two OPF alternatives that confine voltage deviations on the average and as a convex restriction of chance constraints. The trained DNNs can be driven by partial, noisy, or proxy descriptors of the current grid conditions. This is important when OPF has to be solved for an unobservable feeder. DNN weights are trained via back-propagation and upon differentiating the AC power flow equations assuming the network model is known. Otherwise, a gradient-free variant is put forth. The latter is relevant when inverters are controlled by an aggregator having access only to a power flow solver or a digital twin of the feeder. Numerical tests compare the DNN-based inverter control schemes with the optimal inverter setpoints in terms of optimality and feasibility., Comment: To appear in IEEE Transactions on Smart Grid

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is comprised of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. We, therefore, develop a minimal model of cells moving through confined geometries that effectively includes all three types of cytoskeletal filaments with a cell consisting of an actomyosin cortex and a deformable cell nucleus and mechanical connections between the two cortices the outer actomyosin one and the inner nuclear one. By decreasing the amount of vimentin, we find that the cell speed is typically faster for vimentin-null cells as compared to cells with vimentin. Vimentin-null cells also contain more deformed nuclei in confinement. Finally, vimentin affects nucleus positioning within the cell. By positing that as the nucleus position deviates further from the center of mass of the cell, microtubules become more oriented in a particular direction to enhance cell persistence or polarity, we show that vimentin-nulls are more persistent than vimentin-full cells. The enhanced persistence indicates that the vimentin-null cells are more subjugated by the confinement since their internal polarization mechanism that depends on cross-talk of the centrosome with the nucleus and other cytoskeletal connections is diminished. In other words, the vimentin-null cells rely more heavily on external cues. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial-mesenchymal transition., Comment: 16 pages, 13 figures

Aiming for the median solution between cyber-intensive optimal power flow (OPF) solutions and subpar local control, this work advocates deciding inverter injection setpoints using deep neural networks (DNNs). Instead of fitting OPF solutions in a black-box manner, inverter DNNs are naturally integrated with the feeder model and trained to minimize a grid-wide objective subject to inverter and network constraints enforced on the average over uncertain grid conditions. Learning occurs in a quasi-stationary fashion and is posed as a stochastic OPF, handled via stochastic primal-dual updates acting on grid data scenarios. Although trained as a whole, the proposed DNN is operated in a master-slave architecture. Its master part is run at the utility to output a condensed control signal broadcast to all inverters. Its slave parts are implemented by inverters and are driven by the utility signal along with local inverter readings. This novel DNN structure uniquely addresses the small-big data conundrum where utilities collect detailed smart meter readings yet on an hourly basis, while in real time inverters should be driven by local inputs and minimal utility coordination to save on communication. Numerical tests corroborate the efficacy of this physics-aware DNN-based inverter solution over an optimal control policy.

Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow (OPF), thus shifting the computational effort from real-time to offline. Nonetheless, before training this DNN, one has to solve a large number of OPFs to create a labeled dataset. Granted the latter step can still be prohibitive in time-critical applications, this work puts forth an original technique for improving the prediction accuracy of DNNs by taking into account the sensitivities of the OPF minimizers with respect to the OPF parameters. By expanding on multiparametric programming, it is shown that although inverter control problems may exhibit dual degeneracy, the required sensitivities do exist in general and can be computed readily using the output of any standard quadratic program (QP) solver. Numerical tests showcase that sensitivity-informed deep learning can enhance prediction accuracy in terms of mean square error (MSE) by 2-3 orders of magnitude at minimal computational overhead. Improvements are more significant in the small-data regime, where a DNN has to learn to optimize using a few examples. Beyond multiparametric QPs, the approach is currently being generalized to parametric (non)-convex optimization problems., Comment: Manuscript under review

Labelling of human behavior analysis data is a complex and time consuming task. In this paper, a fully automatic technique for labelling an image based gaze behavior dataset for driver gaze zone estimation is proposed. Domain knowledge is added to the data recording paradigm and later labels are generated in an automatic manner using Speech To Text conversion (STT). In order to remove the noise in the STT process due to different illumination and ethnicity of subjects in our data, the speech frequency and energy are analysed. The resultant Driver Gaze in the Wild (DGW) dataset contains 586 recordings, captured during different times of the day including evenings. The large scale dataset contains 338 subjects with an age range of 18-63 years. As the data is recorded in different lighting conditions, an illumination robust layer is proposed in the Convolutional Neural Network (CNN). The extensive experiments show the variance in the dataset resembling real-world conditions and the effectiveness of the proposed CNN pipeline. The proposed network is also fine-tuned for the eye gaze prediction task, which shows the discriminativeness of the representation learnt by our network on the proposed DGW dataset. Project Page: https://sites.google.com/view/drivergazeprediction/home

With increasingly favorable economics and bundling of different grid services, energy storage systems (ESS) are expected to play a key role in integrating renewable generation. This work considers the coordination of ESS owned by customers located at different buses of a distribution grid. Customers participate in frequency regulation and experience energy prices that increase with the total demand. Charging decisions are coupled across time due to battery dynamics, as well as across network nodes due to competitive pricing and voltage regulation constraints. Maximizing the per-user economic benefit while maintaining voltage magnitudes within allowable limits is posed here as a network-constrained game. It is analytically shown that a generalized Nash equilibrium exists and can be expressed as the minimizer of a convex yet infinite-time horizon aggregate optimization problem. To obtain a practical solution, a Lyapunov optimization approach is adopted to design a real-time scheme offering feasible charging decisions with performance guarantees. The proposed method improves over the standard Lyapunov technique via a novel weighting of user costs. By judiciously exploiting the physical grid response, a distributed implementation of the real-time solver is also designed. The features of the novel algorithmic designs are validated using numerical tests on realistic datasets., Comment: Accepted for publication in the IEEE Trans. on Smart Grid