arXiv subjects

Ismail Alkhouri

Publications and source records attributed to Ismail Alkhouri.

At least 19 recordsLinked to original sources

arXiv2026

Parallelizable Gradient-Based Optimization For Multi-Objective MaxCut

Multi-objective combinatorial optimization arises in a wide range of problems and applications, including the canonical multi-objective MaxCut problem. Differentiable single-instance quadratic methods have recently achieved remarkable performance in single-objective combinatorial optimization. In this paper, we develop a differentiable framework for multi-objective MaxCut by combining an adjacency-based quadratic formulation with linear scalarization, thereby reducing the problem to a preference-conditioned single-objective signed-weight MaxCut problem. Theoretically, we characterize the stationary points of the resulting signed-weight formulation and show how they induce preference-conditioned fixed points on the Pareto front. Computationally, unlike conventional heuristics and branch-and-bound methods, our approach is GPU-parallelizable and can therefore benefit from substantial performance speedups. We term our algorithm Multi-objective QUadratic Combinatorial Optimization (MO-QUCO) and its parallelized variant pMO-QUCO. Empirically, across different multi-layered (and weight distributions) graphs, we show that both our CPU-only and GPU-based algorithms outperform SOTA exact and heuristic methods in terms of wall-clock runtime and objective quality. Despite operating under different computational settings, MO-QUCO also outperforms the SOTA quantum method.

cs.DM↗

arXiv2026

Local Minima in Quadratic-Penalty Relaxations of Binary Linear Programs

Many combinatorial optimization problems admit quadratic unconstrained binary formulations (QUBO) which can often be relaxed to the box $[0,1]^n$ and optimized using scalable gradient-based methods. However, the resulting non-convex landscape can often contain local optima that are spurious or infeasible. In this paper, we establish sufficient structural conditions on quadratic penalties that rule out these failures, guaranteeing that every local minimizer of the relaxed problem is both binary and feasible. For each problem we study, we examine existing QUBO formulations when available, identify why they fail when they do, and propose alternative relaxed QUBOs that satisfy our conditions. We show for several common combinatorial problems, including open-pit mining, 0--1 knapsack, and traveling salesman formulations, that these constructions allow gradient-based methods such as projected gradient descent and Adam to be safely applied to obtain valid binary solutions. Our results clarify when differentiable optimization is a reliable local solver for quadratic combinatorial objectives.

cs.DM↗

arXiv2026

Dynamic MRI Reconstruction Via Dual Deep Priors and Low-Rank Plus Sparse Modeling

Dynamic MRI reconstruction from undersampled measurements is a challenging inverse problem that requires preserving both spatial reconstruction quality and temporal consistency across the frames of the cine series. While recent learning-based approaches achieve strong performance, they heavily rely on large training, mostly fully sampled, datasets, and may otherwise generalize poorly. In contrast, training-data-free methods such as deep image prior (DIP) adapt directly to individual scans but often fail to fully exploit temporal structure and are prone to overfitting. They are particularly attractive for dynamic MRI due to the limited large, public, high-quality datasets. In this work, we propose a structured DIP framework for dynamic MRI reconstruction that explicitly models spatiotemporal correlations through a low-rank plus sparse (L+S) decomposition. Instead of directly reconstructing the cine image series, we parameterize the low-rank background and sparse dynamic components using two DIP untrained convolutional neural networks, jointly optimized using accelerated extrapolated ADMM (eADMM). This formulation combines the implicit regularization of DIP with the interpretability of classical L+S regularization. We provide a convergence analysis for the proposed eADMM algorithm in the presence of DIP-based nonconvex parameterizations. In particular, we establish a sufficient descent property and show that every cluster point of the generated sequence is a critical point of the associated Lyapunov function. Across various acceleration factors, our numerical results demonstrate that the proposed method consistently outperforms classical reconstruction and existing supervised and unsupervised MRI reconstruction techniques.

eess.IV↗

arXiv2026

ForcingDAS: Unified and Robust Data Assimilation via Diffusion Forcing

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on frame-to-frame transition models. However, these models are fragile when observations are non-Markovian (when they form only a partial slice of a higher-dimensional latent state as in real-world weather data): they tend to accumulate errors over long horizons. At the same time, learned DA methods typically commit to a single regime, either filtering (nowcasting, real-time forecasting) or smoothing (retrospective reanalysis), which splits what should be a shared prior across application-specific pipelines. To address both issues, we introduce ForcingDAS, a unified and robust DA framework. Built on Diffusion Forcing with an independent noise level assigned to each frame, ForcingDAS learns a joint-trajectory prior instead of frame-to-frame transitions. This allows it to capture long-horizon temporal dependencies and reduce error accumulation. In addition, the same trained model spans the full filtering to smoothing spectrum at inference time. Specifically, nowcasting, fixed-lag smoothing, and batch reanalysis are selected through the inference schedule alone, without retraining. We evaluate ForcingDAS on 2D Navier-Stokes vorticity, precipitation nowcasting, and global atmospheric state estimation. Across all settings, a single model is competitive with or outperforms both learned and classical baselines that are specialized for individual regimes, with the largest gains observed on real-world weather benchmarks.

eess.IV↗

arXiv2026

Mutation-Guided Differentiable Quadratic Combinatorial Optimization

Recent studies suggest that gradient-based methods applied to relaxed box-constrained Quadratic Unconstrained Binary Optimization (QUBO) formulations can outperform classical heuristics in some large-scale regimes, often relying on heavy parallelization. However, these methods still underperform heuristics in other settings. In this work, we clarify this apparent discrepancy through a detailed analysis of the relaxed non-convex QUBO local maxima for both the Maximum Independent Set (MIS) and Maximum Cut (MaxCut) problems, and by introducing a new quadratic objective for MaxCut. Motivated by this analysis, we propose a mutation-based differentiable global reset algorithm, combined with local search to escape local maxima. We term our approach mQO, standing for mutation-based Quadratic combinatorial Optimization. The proposed strategy dramatically improves the performance of gradient-based solvers without heavy reliance on GPU parallelized initializations, indicating that stalling, rather than model capacity or compute, is the dominant bottleneck. As a result, on large-scale graphs, mQO achieves superior performance against state-of-the-art heuristics, commercial integer programming solvers, and recent GPU methods.

cs.DM↗

arXiv2026

GaloisSAT: Differentiable Boolean Satisfiability Solving via Finite Field Algebra

Boolean satisfiability (SAT) problem, the first problem proven to be NP-complete, has become a fundamental challenge in computational complexity, with widespread applications in optimization and verification across many domains. Despite significant algorithmic advances over the past two decades, the performance of SAT solvers has improved at a limited pace. Notably, the 2025 competition winner shows only about a 2X improvement over the 2006 winner in SAT Competition performance after nearly 20 years of effort. This paper introduces GaloisSAT, a novel hybrid GPU-CPU SAT solver that integrates a differentiable SAT solving engine powered by modern machine learning infrastructure on GPUs, followed by a traditional CDCL-based SAT solving stage on CPUs. GaloisSAT is benchmarked against the latest versions of state-of-the-art solvers, Kissat and CaDiCaL, using the SAT Competition 2024 benchmark suite. Results demonstrate substantial improvements in the official SAT Competition metric PAR-2 (penalized average runtime with a timeout of 5,000 seconds and a penalty factor of 2). Specifically, GaloisSAT achieves an 8.41X speedup in the satisfiable category and a 1.29X speedup in the unsatisfiable category compared to the strongest baselines.

cs.LO↗

arXiv2025

Tada-DIP: Input-adaptive Deep Image Prior for One-shot 3D Image Reconstruction

Deep Image Prior (DIP) has recently emerged as a promising one-shot neural-network based image reconstruction method. However, DIP has seen limited application to 3D image reconstruction problems. In this work, we introduce Tada-DIP, a highly effective and fully 3D DIP method for solving 3D inverse problems. By combining input-adaptation and denoising regularization, Tada-DIP produces high-quality 3D reconstructions while avoiding the overfitting phenomenon that is common in DIP. Experiments on sparse-view X-ray computed tomography reconstruction validate the effectiveness of the proposed method, demonstrating that Tada-DIP produces much better reconstructions than training-data-free baselines and achieves reconstruction performance on par with a supervised network trained using a large dataset with fully-sampled volumes.

eess.IV↗

arXiv2025

NERD: Network-Regularized Diffusion Sampling For 3D Computed Tomography

Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces measurement consistency, forward diffusion consistency, and both step-wise and backward diffusion consistency. However, these methods have only considered 2D reconstruction tasks and do not directly extend to 3D image reconstruction problems, such as in Computed Tomography (CT). To bridge this gap, we propose NEtwork-Regularized diffusion sampling for 3D CT (NERD) by incorporating an L1 regularization into the optimization objective. This regularizer encourages spatial continuity across adjacent slices, reducing inter-slice artifacts and promoting coherent volumetric reconstructions. Additionally, we introduce two efficient optimization strategies to solve the resulting objective: one based on the Alternating Direction Method of Multipliers (ADMM) and another based on the Primal-Dual Hybrid Gradient (PDHG) method. Experiments on medical 3D CT data demonstrate that our approach achieves either state-of-the-art or highly competitive results.

eess.IV↗

arXiv2025

A Scalable Lift-and-Project Differentiable Approach For the Maximum Cut Problem

We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is not a machine learning method and does not require training data. Starting from a continuous relaxation of the classical quadratic binary formulation, we present a parallelized strategy that explores multiple initialization vectors in batch. We analyze the relaxed objective, showing it is convex and has fixed-points corresponding to local optima, particularly at boundary points, highlighting a key challenge in non-convex optimization. To improve exploration, we introduce a lifted quadratic formulation that over-parameterizes the solution space. We also provide a theoretical characterization of these lifted fixed-points. Finally, we propose DECO, a dimension-alternating algorithm that switches between the unlifted and lifted formulations, combined with importance-based degree initialization and a population-based evolutionary hyper-parameter search. Experiments on diverse graph families show that our methods attain comparable or superior performance relative to recent neural networks and GPU-accelerated sampling approaches.

cs.DM↗

arXiv2025

A Dataless Reinforcement Learning Approach to Rounding Hyperplane Optimization for Max-Cut

The Maximum Cut (MaxCut) problem is NP-Complete, and obtaining its optimal solution is NP-hard in the worst case. As a result, heuristic-based algorithms are commonly used, though their design often requires significant domain expertise. More recently, learning-based methods trained on large (un)labeled datasets have been proposed; however, these approaches often struggle with generalizability and scalability. A well-known approximation algorithm for MaxCut is the Goemans-Williamson (GW) algorithm, which relaxes the Quadratic Unconstrained Binary Optimization (QUBO) formulation into a semidefinite program (SDP). The GW algorithm then applies hyperplane rounding by uniformly sampling a random hyperplane to convert the SDP solution into binary node assignments. In this paper, we propose a training-data-free approach based on a non-episodic reinforcement learning formulation, in which an agent learns to select improved rounding hyperplanes that yield better cuts than those produced by the GW algorithm. By optimizing over a Markov Decision Process (MDP), our method consistently achieves better cuts across large-scale graphs with varying densities and degree distributions.

cs.LG↗

arXiv2025

Understanding Untrained Deep Models for Inverse Problems: Algorithms and Theory

In recent years, deep learning methods have been extensively developed for inverse imaging problems (IIPs), encompassing supervised, self-supervised, and generative approaches. Most of these methods require large amounts of labeled or unlabeled training data to learn effective models. However, in many practical applications, such as medical image reconstruction, extensive training datasets are often unavailable or limited. A significant milestone in addressing this challenge came in 2018 with the work of Ulyanov et al., which introduced the Deep Image Prior (DIP)--the first training-data-free neural network method for IIPs. Unlike conventional deep learning approaches, DIP requires only a convolutional neural network, the noisy measurements, and a forward operator. By leveraging the implicit regularization of deep networks initialized with random noise, DIP can learn and restore image structures without relying on external datasets. However, a well-known limitation of DIP is its susceptibility to overfitting, primarily due to the over-parameterization of the network. In this tutorial paper, we provide a comprehensive review of DIP, including a theoretical analysis of its training dynamics. We also categorize and discuss recent advancements in DIP-based methods aimed at mitigating overfitting, including techniques such as regularization, network re-parameterization, and early stopping. Furthermore, we discuss approaches that combine DIP with pre-trained neural networks, present empirical comparison results against data-centric methods, and highlight open research questions and future directions.

eess.IV↗

arXiv2024

SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems

Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse problems, the reverse sampling steps are modified to approximately sample from a measurement-conditioned distribution. However, these modifications may be unsuitable for certain settings (e.g., presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates our proposed step-wise and network-regularized backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions (implicitly or explicitly), our sampler requires significantly fewer reverse steps. Therefore, we refer to our method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to SOTA baselines, our experiments across several linear and non-linear tasks (with natural and medical images) demonstrate that SITCOM achieves competitive or superior results in terms of standard similarity metrics and run-time.

eess.IV↗

arXiv2024

Sequential Diffusion-Guided Deep Image Prior For Medical Image Reconstruction

Deep learning (DL) methods have been extensively applied to various image recovery problems, including magnetic resonance imaging (MRI) and computed tomography (CT) reconstruction. Beyond supervised models, other approaches have been recently explored including two key recent schemes: Deep Image Prior (DIP) that is an unsupervised scan-adaptive method that leverages the network architecture as implicit regularization but can suffer from noise overfitting, and diffusion models (DMs), where the sampling procedure of a pre-trained generative model is modified to allow sampling from the measurement-conditioned distribution through approximations. In this paper, we propose combining DIP and DMs for MRI and CT reconstruction, motivated by (i) the impact of the DIP network input and (ii) the use of DMs as diffusion purifiers (DPs). Specifically, we propose a sequential procedure that iteratively optimizes the DIP network with a DM-refined adaptive input using a loss with data consistency and autoencoding terms. We term the approach Sequential Diffusion-Guided DIP (uDiG-DIP). Our experimental results demonstrate that uDiG-DIP achieves superior reconstruction results compared to leading DM-based baselines and the original DIP for MRI and CT tasks.

eess.IV↗

arXiv2024

Differentiable Quadratic Optimization For The Maximum Independent Set Problem

Combinatorial Optimization (CO) addresses many important problems, including the challenging Maximum Independent Set (MIS) problem. Alongside exact and heuristic solvers, differentiable approaches have emerged, often using continuous relaxations of ReLU-based or quadratic objectives. Noting that an MIS in a graph is a Maximum Clique (MC) in its complement, we propose a new quadratic formulation for MIS by incorporating an MC term, improving convergence and exploration. We show that every maximal independent set corresponds to a local minimizer, derive conditions with respect to the MIS size, and characterize stationary points. To tackle the non-convexity of the objective, we propose optimizing several initializations in parallel using momentum-based gradient descent, complemented by an efficient MIS checking criterion derived from our theory. We dub our method as parallelized Clique-Informed Quadratic Optimization for MIS (pCQO-MIS). Our experimental results demonstrate the effectiveness of the proposed method compared to exact, heuristic, sampling, and data-centric approaches. Notably, our method avoids the out-of-distribution tuning and reliance on (un)labeled data required by data-centric methods, while achieving superior MIS sizes and competitive runtime relative to their inference time. Additionally, a key advantage of pCQO-MIS is that, unlike exact and heuristic solvers, the runtime scales only with the number of nodes in the graph, not the number of edges. Our code is available at the GitHub repository: https://github.com/ledenmat/pCQO-mis-benchmark/tree/refactor.

cs.DM↗

arXiv2023

Improving Efficiency of Diffusion Models via Multi-Stage Framework and Tailored Multi-Decoder Architectures

Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new samples (e.g., images). However, their remarkable generative performance is hindered by slow training and sampling. This is due to the necessity of tracking extensive forward and reverse diffusion trajectories, and employing a large model with numerous parameters across multiple timesteps (i.e., noise levels). To tackle these challenges, we present a multi-stage framework inspired by our empirical findings. These observations indicate the advantages of employing distinct parameters tailored to each timestep while retaining universal parameters shared across all time steps. Our approach involves segmenting the time interval into multiple stages where we employ custom multi-decoder U-net architecture that blends time-dependent models with a universally shared encoder. Our framework enables the efficient distribution of computational resources and mitigates inter-stage interference, which substantially improves training efficiency. Extensive numerical experiments affirm the effectiveness of our framework, showcasing significant training and sampling efficiency enhancements on three state-of-the-art diffusion models, including large-scale latent diffusion models. Furthermore, our ablation studies illustrate the impact of two important components in our framework: (i) a novel timestep clustering algorithm for stage division, and (ii) an innovative multi-decoder U-net architecture, seamlessly integrating universal and customized hyperparameters.

cs.CV↗

arXiv2023

Robust MRI Reconstruction by Smoothed Unrolling (SMUG)

As the popularity of deep learning (DL) in the field of magnetic resonance imaging (MRI) continues to rise, recent research has indicated that DL-based MRI reconstruction models might be excessively sensitive to minor input disturbances, including worst-case additive perturbations. This sensitivity often leads to unstable, aliased images. This raises the question of how to devise DL techniques for MRI reconstruction that can be robust to train-test variations. To address this problem, we propose a novel image reconstruction framework, termed Smoothed Unrolling (SMUG), which advances a deep unrolling-based MRI reconstruction model using a randomized smoothing (RS)-based robust learning approach. RS, which improves the tolerance of a model against input noises, has been widely used in the design of adversarial defense approaches for image classification tasks. Yet, we find that the conventional design that applies RS to the entire DL-based MRI model is ineffective. In this paper, we show that SMUG and its variants address the above issue by customizing the RS process based on the unrolling architecture of a DL-based MRI reconstruction model. Compared to the vanilla RS approach, we show that SMUG improves the robustness of MRI reconstruction with respect to a diverse set of instability sources, including worst-case and random noise perturbations to input measurements, varying measurement sampling rates, and different numbers of unrolling steps. Furthermore, we theoretically analyze the robustness of our method in the presence of perturbations.

eess.IV↗

arXiv2023

Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification

Deep learning (DL) techniques have been extensively employed in magnetic resonance imaging (MRI) reconstruction, delivering notable performance enhancements over traditional non-DL methods. Nonetheless, recent studies have identified vulnerabilities in these models during testing, namely, their susceptibility to (\textit{i}) worst-case measurement perturbations and to (\textit{ii}) variations in training/testing settings like acceleration factors and k-space sampling locations. This paper addresses the robustness challenges by leveraging diffusion models. In particular, we present a robustification strategy that improves the resilience of DL-based MRI reconstruction methods by utilizing pretrained diffusion models as noise purifiers. In contrast to conventional robustification methods for DL-based MRI reconstruction, such as adversarial training (AT), our proposed approach eliminates the need to tackle a minimax optimization problem. It only necessitates fine-tuning on purified examples. Our experimental results highlight the efficacy of our approach in mitigating the aforementioned instabilities when compared to leading robustification approaches for deep MRI reconstruction, including AT and randomized smoothing.

eess.IV↗

arXiv2023

On the Robustness of AlphaFold: A COVID-19 Case Study

Protein folding neural networks (PFNNs) such as AlphaFold predict remarkably accurate structures of proteins compared to other approaches. However, the robustness of such networks has heretofore not been explored. This is particularly relevant given the broad social implications of such technologies and the fact that biologically small perturbations in the protein sequence do not generally lead to drastic changes in the protein structure. In this paper, we demonstrate that AlphaFold does not exhibit such robustness despite its high accuracy. This raises the challenge of detecting and quantifying the extent to which these predicted protein structures can be trusted. To measure the robustness of the predicted structures, we utilize (i) the root-mean-square deviation (RMSD) and (ii) the Global Distance Test (GDT) similarity measure between the predicted structure of the original sequence and the structure of its adversarially perturbed version. We prove that the problem of minimally perturbing protein sequences to fool protein folding neural networks is NP-complete. Based on the well-established BLOSUM62 sequence alignment scoring matrix, we generate adversarial protein sequences and show that the RMSD between the predicted protein structure and the structure of the original sequence are very large when the adversarial changes are bounded by (i) 20 units in the BLOSUM62 distance, and (ii) five residues (out of hundreds or thousands of residues) in the given protein sequence. In our experimental evaluation, we consider 111 COVID-19 proteins in the Universal Protein resource (UniProt), a central resource for protein data managed by the European Bioinformatics Institute, Swiss Institute of Bioinformatics, and the US Protein Information Resource. These result in an overall GDT similarity test score average of around 34%, demonstrating a substantial drop in the performance of AlphaFold.

cs.LG↗