Hoang Tran

Abdellah Chkifa, Nick Dexter, Hoang Tran et al.

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly decaying orthonormal expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we present an innovative weighted $\ell_1$ minimization procedure with a precise choice of weights, and a new iterative hard thresholding method, for imposing the downward closed preference. Theoretical results reveal that our computational approaches possess a provably reduced sample complexity compared to existing compressed sensing techniques presented in the literature. In addition, the recovery of the corresponding best approximation using these methods is established through an improved bound for the restricted isometry property. Our analysis represents an extension of the approach for Hadamard matrices in [5] to the general case of continuous bounded orthonormal systems, quantifies the dependence of sample complexity on the successful recovery probability, and provides an estimate on the number of measurements with explicit constants. Numerical examples are provided to support the theoretical results and demonstrate the computational efficiency of the novel weighted $\ell_1$ minimization strategy.

Nick Dexter, Hoang Tran, Clayton Webster

We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a jointly sparse reconstruction problem through the reformulation of the standard basis pursuit denoising, where the set of jointly sparse vectors is infinite. To achieve global reconstruction of sparse solutions to parameterized elliptic PDEs over both physical and parametric domains, we combine the standard measurement scheme developed for compressed sensing in the context of bounded orthonormal systems with a novel mixed-norm based $\ell_1$ regularization method that exploits both energy and sparsity. In addition, we are able to prove that, with minimal sample complexity, error estimates comparable to the best $s$-term and quasi-optimal approximations are achievable, while requiring only a priori bounds on polynomial truncation error with respect to the energy norm. Finally, we perform extensive numerical experiments on several high-dimensional parameterized elliptic PDE models to demonstrate the superior recovery properties of the proposed approach.

Armenak Petrosyan, Hoang Tran, Clayton Webster

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This result reveals a reduction in the computational complexity of the original problem and enables a simple implementation of joint sparse recovery algorithms for full-rank setting. Secondly, we propose a new method for joint sparse recovery in the form of a non-convex optimization problem on a non-compact Stiefel manifold. In our numerical experiments our method outperforms the commonly used $\ell_{2,1}$ minimization in the sense that much fewer measurements are required for accurate sparse reconstructions. We postulate this approach possesses the desirable rank aware property, that is, being able to take advantage of the rank of the unknown matrix to improve the recovery.

Hoang Tran, Ashok Cutkosky

We introduce new algorithms and convergence guarantees for privacy-preserving non-convex Empirical Risk Minimization (ERM) on smooth $d$-dimensional objectives. We develop an improved sensitivity analysis of stochastic gradient descent on smooth objectives that exploits the recurrence of examples in different epochs. By combining this new approach with recent analysis of momentum with private aggregation techniques, we provide an $(ε,δ)$-differential private algorithm that finds a gradient of norm $\tilde O\left(\frac{d^{1/3}}{(εN)^{2/3}}\right)$ in $O\left(\frac{N^{7/3}ε^{4/3}}{d^{2/3}}\right)$ gradient evaluations, improving the previous best gradient bound of $\tilde O\left(\frac{d^{1/4}}{\sqrt{εN}}\right)$.

Qinzi Zhang, Hoang Tran, Ashok Cutkosky

We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $ε$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + \sqrt{d}/εT)$ on smooth losses in linear time, forming a direct analogy to the classical non-private "online-to-batch" conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.

Hoang Tran, Jorge Ramirez, Jiayi Wang et al.

Fine-tuning adapts a pretrained machine learning model to a small, sensitive dataset, but this process risks memorizing individual new data points, making the model vulnerable to adversaries who seek to extract sensitive information. In this work, we develop a randomized algorithm based on the exponential mechanism for fine-tuning while ensuring differential privacy. Our key idea is to construct a simple utility function that combines a local quadratic approximation of the pretrained model with information from the new dataset. The resulting exponential mechanism admits exact sampling from a multivariate normal distribution in closed form. We establish theoretical privacy guarantees, sensitivity bounds, and accuracy estimations for our method. We further introduce a random-projection strategy that makes the approach scalable to high-dimensional models. Numerical experiments on the MNIST benchmark and the MIMIC clinical dataset demonstrate competitive performance against existing differentially private fine-tuning techniques.

Xingyao Wang, Simon Rosenberg, Juan Michelini et al.

Agents are now used widely in the process of software development, but building production-ready software engineering agents is a complex task. Deploying software agents effectively requires flexibility in implementation and experimentation, reliable and secure execution, and interfaces for users to interact with agents. In this paper, we present the OpenHands Software Agent SDK, a toolkit for implementing software development agents that satisfy these desiderata. This toolkit is a complete architectural redesign of the agent components of the popular OpenHands framework for software development agents, which has 64k+ GitHub stars. To achieve flexibility, we design a simple interface for implementing agents that requires only a few lines of code in the default case, but is easily extensible to more complex, full-featured agents with features such as custom tools, memory management, and more. For security and reliability, it delivers seamless local-to-remote execution portability, integrated REST/WebSocket services. For interaction with human users, it can connect directly to a variety of interfaces, such as visual workspaces (VS Code, VNC, browser), command-line interfaces, and APIs. Compared with existing SDKs from OpenAI, Claude, and Google, OpenHands uniquely integrates native sandboxed execution, lifecycle control, model-agnostic multi-LLM routing, and built-in security analysis. Empirical results on SWE-Bench Verified and GAIA benchmarks demonstrate strong performance. Put together, these elements allow the OpenHands Software Agent SDK to provide a practical foundation for prototyping, unlocking new classes of custom applications, and reliably deploying agents at scale.

Armenak Petrosyan, Konstantin Pieper, Hoang Tran

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used $\ell_{2,1}$ regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.

Hoang Tran, Qinzi Zhang, Ashok Cutkosky

There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of different assumptions, which are themselves often chosen based on a rough combination of intuitive match to practice and analytical convenience. In this paper, we carefully measure the degree to which the standard optimization analyses are capable of explaining modern algorithms. To do this, we develop new empirical metrics that compare real optimization behavior with analytically predicted behavior. Our investigation is notable for its tight integration with modern optimization analysis: rather than simply checking high-level assumptions made in the analysis (e.g. smoothness), we also verify key low-level identities used by the analysis to explain optimization behavior that might hold even if the high-level motivating assumptions do not. Notably, we find that smoothness-based analyses fail in practice under most scenarios, but the key identities commonly used in convex-optimization analyses often hold in practice despite the objective's global non-convexity.

Boris Mocialov, Eirik Eythorsson, Reza Parseh et al.

This work takes a look at data models often used in digital twins and presents preliminary results specifically from surface reconstruction and semantic segmentation models trained using simulated data. This work is expected to serve as a ground work for future endeavours in data contextualisation inside a digital twin.

Siming Liang, Hoang Tran, Feng Bao et al.

Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems.

Radhika Dua, Nikita Saxena, Aditi Agarwal et al.

Agricultural landscapes are quite complex, especially in the Global South where fields are smaller, and agricultural practices are more varied. In this paper we report on our progress in digitizing the agricultural landscape (natural and man-made) in our study region of India. We use high resolution imagery and a UNet style segmentation model to generate the first of its kind national-scale multi-class panoptic segmentation output. Through this work we have been able to identify individual fields across 151.7M hectares, and delineating key features such as water resources and vegetation. We share how this output was validated by our team and externally by downstream users, including some sample use cases that can lead to targeted data driven decision making. We believe this dataset will contribute towards digitizing agriculture by generating the foundational baselayer.

Hoang Tran, Zezhong Zhang, Feng Bao et al.

We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling methods, are effective for sampling from single-mode distributions in high-dimensional spaces. However, these methods struggle to produce samples with the correct proportions for each mode in multimodal distributions, especially for distributions with well separated modes. To address the challenges posed by multimodality, we adopt a divide-and-conquer strategy. We start by minimizing the energy function with initial guesses uniformly distributed within the prior domain to identify all the modes of the energy function. Then, we train a classifier to segment the domain corresponding to each mode. After the domain decomposition, we train a diffusion-model-assisted generative model for each identified mode within its support. Once each mode is characterized, we employ bridge sampling to estimate the normalizing constant, allowing us to directly adjust the ratios between the modes. Our numerical examples demonstrate that the proposed framework can effectively handle multimodal distributions with varying mode shapes in up to 100 dimensions. An application to Bayesian inverse problem for partial differential equations is also provided.

Qinzi Zhang, Hoang Tran, Ashok Cutkosky

We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(α,αρ^2/2)$-Rényi differential privacy and finds a $(δ,ε)$-stationary point so long as $M=\tildeΩ\left(\frac{d}{δε^3} + \frac{d^{3/2}}{ρδε^2}\right)$. This matches the optimal complexity of its non-private zeroth-order analog. Notably, although the objective is not smooth, we have privacy ``for free'' whenever $ρ\ge \sqrt{d}ε$.

Majdi I. Radaideh, Hoang Tran, Lianshan Lin et al.

The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source (SNS). We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large-scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The experiments and results of the two methods show a very good agreement for the solid mechanics simulation of the mercury spallation target. The proposed methods are used to calibrate the tensile cutoff threshold, mercury density, and mercury speed of sound during intense proton pulse experiments. Using strain experimental data from the mercury target sensors, the newly calibrated simulations achieve 7\% average improvement on the signal prediction accuracy and 8\% reduction in mean absolute error compared to previously reported reference parameters, with some sensors experiencing up to 30\% improvement. The proposed calibrated simulations can significantly aid in fatigue analysis to estimate the mercury target lifetime and integrity, which reduces abrupt target failure and saves a tremendous amount of costs. However, an important conclusion from this work points out to a deficiency in the current constitutive model based on the equation of state in capturing the full physics of the spallation reaction. Given that some of the calibrated parameters that show a good agreement with the experimental data can be nonphysical mercury properties, we need a more advanced two-phase flow model to capture bubble dynamics and mercury cavitation.

Hoang Tran, Ashok Cutkosky

We develop a new algorithm for non-convex stochastic optimization that finds an $ε$-critical point in the optimal $O(ε^{-3})$ stochastic gradient and Hessian-vector product computations. Our algorithm uses Hessian-vector products to "correct" a bias term in the momentum of SGD with momentum. This leads to better gradient estimates in a manner analogous to variance reduction methods. In contrast to prior work, we do not require excessively large batch sizes, and are able to provide an adaptive algorithm whose convergence rate automatically improves with decreasing variance in the gradient estimates. We validate our results on a variety of large-scale deep learning architectures and benchmarks tasks.

Hoang Tran, Guannan Zhang

The local gradient points to the direction of the steepest slope in an infinitesimal neighborhood. An optimizer guided by the local gradient is often trapped in local optima when the loss landscape is multi-modal. A directional Gaussian smoothing (DGS) approach was recently proposed in (Zhang et al., 2020) and used to define a truly nonlocal gradient, referred to as the DGS gradient, for high-dimensional black-box optimization. Promising results show that replacing the traditional local gradient with the DGS gradient can significantly improve the performance of gradient-based methods in optimizing highly multi-modal loss functions. However, the optimal performance of the DGS gradient may rely on fine tuning of two important hyper-parameters, i.e., the smoothing radius and the learning rate. In this paper, we present a simple, yet ingenious and efficient adaptive approach for optimization with the DGS gradient, which removes the need of hyper-parameter fine tuning. Since the DGS gradient generally points to a good search direction, we perform a line search along the DGS direction to determine the step size at each iteration. The learned step size in turn will inform us of the scale of function landscape in the surrounding area, based on which we adjust the smoothing radius accordingly for the next iteration. We present experimental results on high-dimensional benchmark functions, an airfoil design problem and a game content generation problem. The AdaDGS method has shown superior performance over several the state-of-the-art black-box optimization methods.

Yiming Xu, Akil Narayan, Hoang Tran et al.

We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is easily satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare $\ell_1/\ell_2$ with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach \emph{support selection}, and we demonstrate that it empirically improves the performance of existing $\ell_1/\ell_2$ algorithms.

Jiaxing Zhang, Hoang Tran, Guannan Zhang

Evolution strategy (ES) has been shown great promise in many challenging reinforcement learning (RL) tasks, rivaling other state-of-the-art deep RL methods. Yet, there are two limitations in the current ES practice that may hinder its otherwise further capabilities. First, most current methods rely on Monte Carlo type gradient estimators to suggest search direction, where the policy parameter is, in general, randomly sampled. Due to the low accuracy of such estimators, the RL training may suffer from slow convergence and require more iterations to reach optimal solution. Secondly, the landscape of reward functions can be deceptive and contains many local maxima, causing ES algorithms to prematurely converge and be unable to explore other parts of the parameter space with potentially greater rewards. In this work, we employ a Directional Gaussian Smoothing Evolutionary Strategy (DGS-ES) to accelerate RL training, which is well-suited to address these two challenges with its ability to i) provide gradient estimates with high accuracy, and ii) find nonlocal search direction which lays stress on large-scale variation of the reward function and disregards local fluctuation. Through several benchmark RL tasks demonstrated herein, we show that DGS-ES is highly scalable, possesses superior wall-clock time, and achieves competitive reward scores to other popular policy gradient and ES approaches.

Jiaxin Zhang, Hoang Tran, Dan Lu et al.

We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with $d$-dimensional Gaussian smoothing suffer from the curse of dimensionality due to the high variance of Monte Carlo (MC) based gradient estimators. To control the variance, Gaussian smoothing is usually limited in a small region, so existing ES methods lack nonlocal exploration ability required for escaping from local minima. We develop a nonlocal gradient operator with directional Gaussian smoothing (DGS) to address this challenge. The DGS conducts 1D nonlocal explorations along $d$ orthogonal directions in $\mathbb{R}^d$, each of which defines a nonlocal directional derivative as a 1D integral. We then use Gauss-Hermite quadrature, instead of MC sampling, to estimate the $d$ 1D integrals to ensure high accuracy (i.e., small variance). Our method enables effective nonlocal exploration to facilitate the global search in high-dimensional optimization. We demonstrate the superior performance of our method in three sets of examples, including benchmark functions for global optimization, and real-world science and engineering applications.

Nick Dexter, Hoang Tran, Clayton Webster

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based $\ell_1$ regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Yiyuan She, Hoang Tran

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing the parameters across all folds may result in an inconsistency issue, and it is more appropriate to cross-validate projection-selection patterns to obtain the best coefficient estimate. Our in-sample error studies in jointly sparse and rank-deficient models lead to a new class of information criteria with four scale-free forms to bypass the estimation of the noise level. By use of an identity, we propose a novel scale-free calibration to help cross-validation achieve the minimax optimal error rate non-asymptotically. Experiments support the efficacy of the proposed methods.

Hoang Tran, Clayton Webster

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using $\ell_1$ minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form $m \gtrsim Θ^2 s \times \textit{log factors}$ have been relied on to determine the minimum number of samples $m$ that guarantees successful reconstruction of $s$-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound $Θ$ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. In this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for $s$-sparse Legendre expansions, $$ m \gtrsim {s^2} \times \textit{log factors}, $$ which is independent of $Θ$. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in [Bou14,CDTW15], to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.