arXiv subjects

Neeraj Sarna

Publications and source records attributed to Neeraj Sarna.

16 recordsLinked to original sources

arXiv2025

Copyright Infringement Risk Reduction via Chain-of-Thought and Task Instruction Prompting

Large scale text-to-image generation models can memorize and reproduce their training dataset. Since the training dataset often contains copyrighted material, reproduction of training dataset poses a copyright infringement risk, which could result in legal liabilities and financial losses for both the AI user and the developer. The current works explores the potential of chain-of-thought and task instruction prompting in reducing copyrighted content generation. To this end, we present a formulation that combines these two techniques with two other copyright mitigation strategies: a) negative prompting, and b) prompt re-writing. We study the generated images in terms their similarity to a copyrighted image and their relevance of the user input. We present numerical experiments on a variety of models and provide insights on the effectiveness of the aforementioned techniques for varying model complexity.

cs.LG↗

arXiv2025

Counterfactually Fair Conformal Prediction

While counterfactual fairness of point predictors is well studied, its extension to prediction sets--central to fair decision-making under uncertainty--remains underexplored. On the other hand, conformal prediction (CP) provides efficient, distribution-free, finite-sample valid prediction sets, yet does not ensure counterfactual fairness. We close this gap by developing Counterfactually Fair Conformal Prediction (CF-CP) that produces counterfactually fair prediction sets. Through symmetrization of conformity scores across protected-attribute interventions, we prove that CF-CP results in counterfactually fair prediction sets while maintaining the marginal coverage property. Furthermore, we empirically demonstrate that on both synthetic and real datasets, across regression and classification tasks, CF-CP achieves the desired counterfactual fairness and meets the target coverage rate with minimal increase in prediction set size. CF-CP offers a simple, training-free route to counterfactually fair uncertainty quantification.

cs.LG↗

arXiv2025

Domain-Shift-Aware Conformal Prediction for Large Language Models

Large language models have achieved impressive performance across diverse tasks. However, their tendency to produce overconfident and factually incorrect outputs, known as hallucinations, poses risks in real-world applications. Conformal prediction provides finite-sample, distribution-free coverage guarantees, but standard conformal prediction breaks down under domain shift, often leading to under-coverage and unreliable prediction sets. We propose a new framework called Domain-Shift-Aware Conformal Prediction (DS-CP). Our framework adapts conformal prediction to large language models under domain shift, by systematically reweighting calibration samples based on their proximity to the test prompt, thereby preserving validity while enhancing adaptivity. Our theoretical analysis and experiments on the MMLU benchmark demonstrate that the proposed method delivers more reliable coverage than standard conformal prediction, especially under substantial distribution shifts, while maintaining efficiency. This provides a practical step toward trustworthy uncertainty quantification for large language models in real-world deployment.

stat.ML↗

arXiv2025

Safer Prompts: Reducing Risks from Memorization in Visual Generative AI

Visual Generative AI models have demonstrated remarkable capability in generating high-quality images from user inputs like text prompts. However, because these models have billions of parameters, they risk memorizing certain parts of the training data and reproducing the memorized content. Memorization often raises concerns about safety of such models -- usually involving intellectual property (IP) infringement risk -- and deters their large scale adoption. In this paper, we evaluate the effectiveness of prompt engineering techniques in reducing memorization risk in image generation. Our findings demonstrate the effectiveness of prompt engineering in reducing the similarity between generated images and the training data of diffusion models, while maintaining relevance and aestheticity of the generated output.

cs.CV↗

arXiv2025

Quantifying Correlations of Machine Learning Models

Machine Learning models are being extensively used in safety critical applications where errors from these models could cause harm to the user. Such risks are amplified when multiple machine learning models, which are deployed concurrently, interact and make errors simultaneously. This paper explores three scenarios where error correlations between multiple models arise, resulting in such aggregated risks. Using real-world data, we simulate these scenarios and quantify the correlations in errors of different models. Our findings indicate that aggregated risks are substantial, particularly when models share similar algorithms, training datasets, or foundational models. Overall, we observe that correlations across models are pervasive and likely to intensify with increased reliance on foundational models and widely used public datasets, highlighting the need for effective mitigation strategies to address these challenges.

cs.LG↗

arXiv2024

An In-Depth Examination of Risk Assessment in Multi-Class Classification Algorithms

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or health-related losses. To better anticipate and prepare for such losses, the algorithm user seeks an estimate for the probability that the algorithm miss-classifies a sample. We refer to this task as the risk-assessment. For a variety of models and datasets, we numerically analyze the performance of different methods in solving the risk-assessment problem. We consider two solution strategies: a) calibration techniques that calibrate the output probabilities of classification models to provide accurate probability outputs; and b) a novel approach based upon the prediction interval generation technique of conformal prediction. Our conformal prediction based approach is model and data-distribution agnostic, simple to implement, and provides reasonable results for a variety of use-cases. We compare the different methods on a broad variety of models and datasets.

cs.LG↗

arXiv2023

Distribution-free risk assessment of regression-based machine learning algorithms

Machine learning algorithms have grown in sophistication over the years and are increasingly deployed for real-life applications. However, when using machine learning techniques in practical settings, particularly in high-risk applications such as medicine and engineering, obtaining the failure probability of the predictive model is critical. We refer to this problem as the risk-assessment task. We focus on regression algorithms and the risk-assessment task of computing the probability of the true label lying inside an interval defined around the model's prediction. We solve the risk-assessment problem using the conformal prediction approach, which provides prediction intervals that are guaranteed to contain the true label with a given probability. Using this coverage property, we prove that our approximated failure probability is conservative in the sense that it is not lower than the true failure probability of the ML algorithm. We conduct extensive experiments to empirically study the accuracy of the proposed method for problems with and without covariate shift. Our analysis focuses on different modeling regimes, dataset sizes, and conformal prediction methodologies.

cs.LG↗

arXiv2021

Learning reduced order models from data for hyperbolic PDEs

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of a transformed solution and a de-transformer. Our idea is to learn a ROM for both these objects, which, unlike the solution, are well approximable in a linear reduced space. A ROM for the (untransformed) solution is then recovered via a recomposition. The transformed solution results from composing the solution with a spatial transform that aligns the spatial discontinuities. Furthermore, the de-transformer is the inverse of the spatial transform and lets us recover a ROM for the solution. We consider an image registration technique to compute the spatial transform, and to learn a ROM, we resort to the dynamic mode decomposition (DMD) methodology. Several benchmark problems demonstrate the effectiveness our method in representing the data and as a predictive tool.

math.NA↗

arXiv2021

Data-Driven Model Order Reduction for Problems with Parameter-Dependent Jump-Discontinuities

We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore, are challenging for standard MOR techniques. We build upon the methodology of approximating the map between the parameter domain and the expansion coefficients of the reduced basis via regression. The online stage queries the regression model for the expansion coefficients and recovers a reduced approximation for the solution. We propose to apply this technique to a transformed solution that results from composing the solution with a spatial transform. Unlike the (untransformed) solution, it is sufficiently regular along the parameter domain and thus, is well-approximable in a low-dimensional linear space. To recover an approximation for the (untransformed) solution, we propose an online efficient regression-based technique that approximates the inverse of the spatial transform. Our method features a decoupled online and offline stage, and benchmark problems involving hyperbolic and parabolic equations demonstrate its effectiveness.

math.NA↗

arXiv2021

Hyper-reduction for parametrized transport dominated problems via online-adaptive reduced meshes

We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted spatial domain, and we compute our reduced approximation via residual minimization. To speed-up the residual minimization, we compute and minimize the residual on a (preferably small) subset of the mesh, the so-called reduced mesh. Due to the nonlinearity of our approximation space we show that, similar to the solution, the residual also exhibits transport-type behaviour. To account for this behaviour, we introduce online-adaptivity in the reduced mesh by "moving" it along the spatial domain with parameter dependent shifts. We also present an extension of our method to spatial transforms different from shifting. Numerical experiments showcase the effectiveness of our method and the inaccuracies resulting from a non-adaptive reduced mesh.

math.NA↗

arXiv2021

Stable Boundary Conditions and Discretization for PN Equations

A solution to the linear Boltzmann equation satisfies an energy bound, which reflects a natural fact: The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over time. In this paper, we present boundary conditions (BCs) for the spherical harmonic (PN) approximation, which ensure that this fundamental energy bound is satisfied by the PN approximation. Our BCs are compatible with the characteristic waves of PN equations and determine the incoming waves uniquely. Both, energy bound and compatibility, are shown based on abstract formulations of PN equations and BCs to isolate the necessary structures and properties. The BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step, which is similar to the truncation of the series expansion in the PN method. We show that summation by parts (SBP) finite differences on staggered grids in space and the method of simultaneous approximation terms (SAT) allows to maintain the energy bound also on the semi-discrete level.

math.NA↗

arXiv2020

A Positive and Stable L2-minimization Based Moment Method for the Boltzmann Equation of Gas dynamics

We consider the method-of-moments approach to solve the Boltzmann equation of rarefied gas dynamics, which results in the following moment-closure problem. Given a set of moments, find the underlying probability density function. The moment-closure problem has infinitely many solutions and requires an additional optimality criterion to single-out a unique solution. Motivated from a discontinuous Galerkin velocity discretization, we consider an optimality criterion based upon L2-minimization. To ensure a positive solution to the moment-closure problem, we enforce positivity constraints on L2-minimization. This results in a quadratic optimization problem with moments and positivity constraints. We show that a (Courant-Friedrichs-Lewy) CFL-type condition ensures both the feasibility of the optimization problem and the L2-stability of the moment approximation. Numerical experiments showcase the accuracy of our moment method.

math.NA↗

arXiv2020

Data-Driven Snapshot Calibration via Monotonic Feature Matching

Snapshot matrices of hyperbolic equations have a slow singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular value decay by computing snapshots on a transformed spatial domain, or the so-called snapshot calibration/transformation. We are particularly interested in problems involving shock collision, shock rarefaction-fan collision, shock formation, etc. For such problems, we propose a realizable algorithm to compute the spatial transform using monotonic feature matching. We consider discontinuities and kinks as features, and by carefully partitioning the parameter domain, we ensure that the spatial transform has properties that are desirable both from a theoretical and an implementation standpoint. We use these properties to prove that our method results in a fast m-width decay of a so-called calibrated manifold. A crucial observation we make is that due to calibration, the m-width does not only depend on m but also on the accuracy of the full order model, which is in contrast to elliptic and parabolic problems that do not need calibration. The method we propose only requires the solution snapshots and not the underlying partial differential equation (PDE) and is therefore, data-driven. We perform several numerical experiments to demonstrate the effectiveness of our method.

math.NA↗

arXiv2020

Moment Method for the Boltzmann Equation of Reactive Quaternary Gaseous Mixture

We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad's-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard spheres. Using the collision model, we present an algorithm to compute the moments of the Boltzmann collision operator. Our algorithm is general in the sense that it can be used to compute arbitrary order moments of the collision operator and not just the moments included in the Grad's-14 moment system. For a first-order chemical kinetics, we derive reaction rates for a chemical reaction outside of equilibrium thereby, extending the Arrhenius law that is valid only in equilibrium. We show that the derived reaction rates (i) are consistent in the sense that at equilibrium, we recover the Arrhenius law and (ii) have an explicit dependence on the scalar fourteenth moment, highlighting the importance of considering a fourteen moment system rather than a thirteen one. Through numerical experiments we study the relaxation of the Grad's-14 moment system to the equilibrium state.

physics.comp-ph↗

arXiv2020

Convergence Analysis of the Grad's Hermite Approximation to the Boltzmann Equation

In (Commun Pure Appl Math 2(4):331-407, 1949), Grad proposed a Hermite series expansion for approximating solutions to kinetic equations that have an unbounded velocity space. However, for initial boundary value problems, poorly imposed boundary conditions lead to instabilities in Grad's Hermite expansion, which could result in non-converging solutions. For linear kinetic equations, a method for posing stable boundary conditions was recently proposed for (formally) arbitrary order Hermite approximations. In the present work, we study $L^2$-convergence of these stable Hermite approximations, and prove explicit convergence rates under suitable regularity assumptions on the exact solution. We confirm the presented convergence rates through numerical experiments involving the linearised-BGK equation of rarefied gas dynamics.

math.NA↗

arXiv2017

Stable boundary conditions for the Hermite Discretization of Boltzmann Equation in Multi Physical Space Dimensions

Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one dimensional Boltzmann equation to the Boltzmann equation involving multi-dimensions in physical and velocity space. Criteria for stable boundary conditions, using energy estimates, have been discussed for linear symmetric hyperbolic initial boundary value problems. Since the use of energy estimates requires the hyperbolic system to be symmetric, the symmetric hyperbolicity of the moment equations arising from a Hermite discretization of the Boltzmann equation has been studied. Furthermore, an algorithm to construct a general symmetrizer for an arbitrary order Hermite discretization has been presented. A block structure for the multi-dimensional moment equations has been recognised which has been used to construct stable Onsager boundary conditions. The newly proposed Onsager boundary conditions have been used to study a Poisson heat conduction problem using a higher order Hermite discretization; the results have been compared to those obtained from the Maxwell's accommodation model.

math.NA↗