arXiv subjects

Abhishek Chakraborty

Publications and source records attributed to Abhishek Chakraborty.

At least 19 recordsLinked to original sources

arXiv2026

Randomized Feasibility-Update Algorithms for Stochastic Variational Inequality Problems

This paper considers stochastic monotone variational inequalities whose feasible region is the intersection of a (possibly infinite) number of convex functional level sets. A projection-based approach or direct Lagrangian-based techniques for such problems can be computationally expensive if not impossible to implement. To deal with the problem, we consider randomized methods that avoid the projection step on the whole constraint set by employing random feasibility updates. In particular, we propose and analyze modified stochastic Korpelevich and Popov methods for solving monotone stochastic VIs. We introduce a modified dual gap function and prove the convergence rates with respect to this function. We illustrate the performance of the methods in simulations on a zero-sum matrix game.

math.OC↗

arXiv2026

Component-Level Inverse Design of Transmon Qubits Using Neural Networks

Designing a superconducting qubit to realize specific Hamiltonian parameters typically requires iterating through a time and compute-intensive forward loop in which the designer chooses a layout geometry, simulates it, extracts circuit parameters such as capacitances, and refines the geometry. We study the inverse version of this task using a neural-network workflow that maps target Hamiltonian parameters directly to component-level layout parameters, which we subsequently demonstrate on a planar transmon layout. During training, we pair the inverse model with a frozen forward surrogate model and evaluate the loss in Hamiltonian space rather than in layout-parameter space. In validation against a conventional EM solver, 97% of generated designs produce usable geometries, and the inverse-plus-surrogate pipeline reaches mean percent errors of 0.73% for qubit frequency and 1.58% for anharmonicity, comparable to or below the fabrication and simulation-to-measurement uncertainty expected for academic-process transmon devices of this type. A single pipeline query takes ~60 ms on CPU, versus ~2 min for a conventional EM capacitance extraction on the same hardware, a speedup of approximately 2,000x. Batching minimizes the AI model inference overhead, reducing the runtime to 3.1 microseconds per sample on CPU and 2.6 microseconds per sample on GPU at a batch size of 2048, resulting in speedups of 3.9 x 10^7 and 4.6 x 10^7, respectively, relative to a single conventional CPU EM extraction. Our results indicate that component-level inverse design usefully extends and complements conventional EM simulation, including for small datasets on the order of 1,000 samples.

quant-ph↗

arXiv2026

Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but possibly nonsmooth objective function. To deal with the constraints that are not easy to project on, we use a randomized feasibility algorithm with Polyak steps and a random number of sampled constraints per iteration, while taking (sub)gradient steps to minimize the objective function. For case (i), we prove linear convergence in expectation of the objective function values to any prescribed tolerance using an adaptive stepsize. For case (ii), we develop a fully problem parameter-free and adaptive stepsize scheme that yields an $O(1/\sqrt{T})$ worst-case rate in expectation. The infeasibility of the iterates decreases geometrically with the number of feasibility updates almost surely, while for the averaged iterates, we establish an expected lower bound on the function values relative to the optimal value that depends on the distribution for the random number of sampled constraints. For certain choices of sample-size growth, optimal rates are achieved. Finally, simulations on a Quadratically Constrained Quadratic Programming (QCQP) problem, Support Vector Machines (SVM), and logistic regression with group fairness constraints demonstrate the computational efficiency of our algorithm compared to other state-of-the-art methods.

math.OC↗

arXiv2026

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization

Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in general norm geometries and develop three complementary algorithms. For smooth non-convex objectives, we introduce Distance-Adaptive Muon, whose trust-region radius is set from the radius explored by the trajectory, and prove a stationarity guarantee under a bounded-trajectory assumption. We then turn to star-convex objectives, a tractable model of the favorable global geometry often used to reason about the empirical loss landscapes of deep neural networks, where objective-gap guarantees are possible. In this setting, we first introduce Scale-Calibrated Muon, which keeps Muon's exponential moving average but sets the step length from a local descent certificate computed from the current gradient and momentum. For this method, we prove a last-iterate O(1/T) objective-gap bound under a bounded initial sublevel-set assumption, where the corresponding radius parameter appears only in the analysis and not in the algorithm. Finally, we develop Distance-Free Muon, a recentered trust-region method that uses a scalar distance certificate and a majorized one-dimensional search to select the trust-region radius without requiring the unknown distance from the initialization to a global minimizer. Experiments on Transformer language modeling (GPT-124M/WikiText-103) and image classification (ViT-Tiny/CIFAR-100) show that the proposed adaptive scaling rules reduce sensitivity to manual scale tuning and match or improve tuned fixed-scale Muon baselines under the tested budgets.

cs.LG↗

arXiv2025

GPU-accelerated Effective Hamiltonian Calculator

Effective Hamiltonian calculations for large quantum systems can be both analytically intractable and numerically expensive using standard techniques. In this manuscript, we present numerical techniques inspired by Nonperturbative Analytical Diagonalization (NPAD) and the Magnus expansion for the efficient calculation of effective Hamiltonians. While these tools are appropriate for a wide array of applications, we here demonstrate their utility for models that can be realized in circuit-QED settings. Our numerical techniques are available as an open-source Python package, ${\rm qCH_{eff}}$, which is available on GitHub (https://github.com/NVlabs/qCHeff) and PyPI (https://pypi.org/project/qcheff/). We use the CuPy library for GPU-acceleration and report up to 15x speedup on GPU over CPU for NPAD, and up to 42x speedup for the Magnus expansion (compared to QuTiP), for large system sizes.

quant-ph↗

arXiv2025

Popov Mirror-Prox Method for Variational Inequalities

This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing methods that require prior knowledge of problem-specific parameters, we propose step-size schemes that are entirely parameter-free in both constant and diminishing forms. For stochastic and deterministic monotone VIs, we establish optimal convergence rates in terms of the dual gap function over a bounded constraint set. Additionally, for deterministic VIs with Hölder continuous mapping, we prove convergence in terms of the residual function without requiring a bounded set or a monotone mapping, provided a Minty solution exists. This allows our method to address certain classes of non-monotone VIs. However, knowledge of the Hölder exponent is necessary to achieve the best convergence rates in this case. By extending mirror-prox techniques to mappings with arbitrary polynomial growth, our work bridges an existing gap in the literature. We validate our theoretical findings with empirical results on matrix games, piecewise quadratic functions, and image classification tasks using ResNet-18.

math.OC↗

arXiv2025

Tunable Superconducting Quantum Interference Device Coupler for Fluxonium Qubits

Tunable couplers enable high-fidelity two-qubit gates leveraging high on/off coupling ratios and reduced crosstalk within a single design. We investigate a galvanically connected direct-current superconducting quantum interference device (dc SQUID) as a minimal tunable coupling element for fluxonium qubits. Comparing grounded and floating fluxonium designs, we find that the latter contains an extra sloshing mode that strongly hybridizes with the qubit modes, leading to significant static ZZ crosstalk. In contrast, the grounded design avoids this issue and allows suppression of static ZZ crosstalk using a shunting capacitor. Leveraging fast flux control, we present two schemes to implement two-qubit gates, predicting a $\sqrt{i\text{SWAP}}$-like gate with $99.9\%$ open-system fidelity in less than 6 nanoseconds assuming modest relaxation and dephasing rates.

quant-ph↗

arXiv2025

Quantum-enhanced photocell based on GaN quantum dots

In this work, we propose an efficient quantum-enhanced solid-state photocell based on GaN quantum dots. We exploit the strong built-in electric field in GaN QDs and excitonic dipole-dipole coupling between adjacent QDs to break detailed balance, leading to enhanced device performance. This mechanism is significantly stronger than Fano interference, and our results demonstrate that such a photocell exhibits increased photovoltage and photocurrent compared to its classical counterparts. Numerical simulations further show that the efficiency remains positive and saturates at a finite value for multi-quantum dot systems. The proposed quantum photocell represents a promising step towards harnessing quantum effects in practical energy-harvesting devices.

quant-ph↗

arXiv2025

Demonstrating Superresolution in Radar Range Estimation Using a Denoising Autoencoder

We apply machine learning methods to demonstrate range superresolution in remote sensing radar detection. Specifically, we implement a denoising autoencoder to estimate the distance between two equal intensity scatterers in the subwavelength regime. The machine learning models are trained on waveforms subject to a bandlimit constraint such that ranges much smaller than the inverse bandlimit are optimized in their precision. The autoencoder achieves effective dimensionality reduction, with the bottleneck layer exhibiting a strong and consistent correlation with the true scatterer separation. We confirm reproducibility across different training sessions and network initializations by analyzing the scaled encoder outputs and their robustness to noise. We investigate the behavior of the bottleneck layer for the following types of pulses: a traditional sinc pulse, a bandlimited triangle-type pulse, and a theoretically near-optimal pulse created from a spherical Bessel function basis. The Bessel signal performs best, followed by the triangle wave, with the sinc signal performing worst, highlighting the crucial role of signal design in the success of machine-learning-based range resolution.

eess.SP↗

arXiv2024

Uncovering Software-Based Power Side-Channel Attacks on Apple M1/M2 Systems

Traditionally, power side-channel analysis requires physical access to the target device, as well as specialized devices to measure the power consumption with enough precision. Recently research has shown that on x86 platforms, on-chip power meter capabilities exposed to a software interface might be used for power side-channel attacks without physical access. In this paper, we show that such software-based power side-channel attack is also applicable on Apple silicon (e.g., M1/M2 platforms), exploiting the System Management Controller (SMC) and its power-related keys, which provides access to the on-chip power meters through a software interface to user space software. We observed data-dependent power consumption reporting from such SMC keys and analyzed the correlations between the power consumption and the processed data. Our work also demonstrated how an unprivileged user mode application successfully recovers bytes from an AES encryption key from a cryptographic service supported by a kernel mode driver in MacOS. We have also studied the feasibility of performing frequency throttling side-channel attack on Apple silicon. Furthermore, we discuss the impact of software-based power side-channels in the industry, possible countermeasures, and the overall implications of software interfaces for modern on-chip power management systems.

cs.CR↗

arXiv2024

Popov Mirror-Prox for solving Variational Inequalities

We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its implementation with Popov method updates. We provide convergence rate analysis of our proposed method for a monotone VI with a Lipschitz continuous mapping. We establish a convergence rate of $O(1/t)$, in terms of the number $t$ of iterations, for the dual gap function. Simulations on a two player matrix game corroborate our findings.

math.OC↗

arXiv2024

Randomized Feasibility-Update Algorithms for Variational Inequality Problems

This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly infinite) number of convex functional level sets. A direct projection-based approach or Lagrangian-based techniques for such a problem can be computationally expensive if not impossible to implement. To deal with the problem, we consider randomized methods that avoid the projection step on the whole constraint set by employing random feasibility updates. In particular, we propose and analyze such random methods for solving VIs based on the projection method, Korpelevich method, and Popov method. We establish the almost sure convergence of the methods and, also, provide their convergence rate guarantees. We illustrate the performance of the methods in simulations for two-agent games.

math.OC↗

arXiv2023

Synchronization gauge field, standing waves and one-way-speed of light

The absolute nature of many fundamental predictions of the theory of special relativity, including the relativity of simultaneity, has been questioned in the literature owing to the choice of distant clock synchronization process in the theory. Here we discuss the consequences of Anderson-Vetharaniam-Stedman (AVS) conventionality synchronization gauge, which reflects the choice of synchronization convention, on the standing wave observable. We found that although the position of the node(s) is gauge invariant and remain the same as in the standard case of the stationary wave formation following the Einstein synchronization, the anti-node(s) becomes a gauge dependent (conventional) element and the resulting wave travels between two nodes, contrary to the experimental observation. The experimental detection of standing wave substantiates that the one-way velocity is equal to the round-trip velocity implying the uniqueness of the Einstein synchronization convention. The present analysis thus eliminates the (unphysical) synchronization gauge freedom of special relativity.

physics.class-ph↗

arXiv2023

Supergrowth and sub-wavelength object imaging

We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its largest wavenumber. We identify the superoscillating and supergrowing regions of a canonical oscillatory function and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging.

physics.optics↗

arXiv2023

Frequency Throttling Side-Channel Attack

Modern processors dynamically control their operating frequency to optimize resource utilization, maximize energy savings, and conform to system-defined constraints. If, during the execution of a software workload, the running average of any electrical or thermal parameter exceeds its corresponding predefined threshold value, the power management architecture will reactively adjust CPU frequency to ensure safe operating conditions. In this paper, we demonstrate how such power management-based frequency throttling activity forms a source of timing side-channel information leakage, which can be exploited by an attacker to infer secret data even from a constant-cycle victim workload. The proposed frequency throttling side-channel attack can be launched by both kernel-space and user-space attackers, thus compromising security guarantees provided by isolation boundaries. We validate our attack methodology across different systems and threat models by performing experiments on a constant-cycle implementation of AES algorithm based on AES-NI instructions. The results of our experimental evaluations demonstrate that the attacker can successfully recover all bytes of an AES key by measuring encryption execution times. Finally, we discuss different options to mitigate the threat posed by frequency throttling side-channel attacks, as well as their advantages and disadvantages.

cs.CR↗

arXiv2022

A quantum algorithm to estimate the closeness to the Strict Avalanche criterion in Boolean functions

We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean function oracle, where $n$ is the number of input variables, this is fewer than the queries required by the classical algorithm to perform the same task. We compare our approach with other quantum algorithms that may be used for estimating the closeness to SAC and it is shown our algorithm verifies SAC with the fewest possible calls to quantum oracle and requires the fewest samples for a given confidence bound.

cs.DS↗

arXiv2022

DynaMarks: Defending Against Deep Learning Model Extraction Using Dynamic Watermarking

The functionality of a deep learning (DL) model can be stolen via model extraction where an attacker obtains a surrogate model by utilizing the responses from a prediction API of the original model. In this work, we propose a novel watermarking technique called DynaMarks to protect the intellectual property (IP) of DL models against such model extraction attacks in a black-box setting. Unlike existing approaches, DynaMarks does not alter the training process of the original model but rather embeds watermark into a surrogate model by dynamically changing the output responses from the original model prediction API based on certain secret parameters at inference runtime. The experimental outcomes on Fashion MNIST, CIFAR-10, and ImageNet datasets demonstrate the efficacy of DynaMarks scheme to watermark surrogate models while preserving the accuracies of the original models deployed in edge devices. In addition, we also perform experiments to evaluate the robustness of DynaMarks against various watermark removal strategies, thus allowing a DL model owner to reliably prove model ownership.

cs.CR↗

arXiv2022

Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descent

We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear interpolation, we hypothesize that the search space is a Reproducing Kernel Hilbert Space (RKHS). We develop first and second-order variants of stochastic mirror descent employing (i) \emph{pseudo-gradients} and (ii) complexity-reducing projections. Compressive projection in the first-order scheme is executed via kernel orthogonal matching pursuit (KOMP), which overcomes the fact that the vanilla RKHS parameterization grows unbounded with the iteration index in the stochastic setting. Moreover, pseudo-gradients are needed when gradient estimates for cost are only computable up to some numerical error, which arise in, e.g., integral approximations. Under constant step-size and compression budget, we establish tradeoffs between the radius of convergence of the expected sub-optimality and the projection budget parameter, as well as non-asymptotic bounds on the model complexity. To refine the solution's precision, we develop a second-order extension which employs recursively averaged pseudo-gradient outer-products to approximate the Hessian inverse, whose convergence in mean is established under an additional eigenvalue decay condition on the Hessian of the optimal RKHS element, which is unique to this work. Experiments demonstrate favorable performance on inhomogeneous Poisson Process intensity estimation in practice.

stat.ML↗