arXiv subjects

El Houcine Bergou

Publications and source records attributed to El Houcine Bergou.

At least 19 recordsLinked to original sources

arXiv2026

TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning

Full-parameter fine-tuning of large language models (LLMs) incurs substantial optimizer state memory overhead, limiting the model sizes that fit on modern GPUs. Existing approaches either compress optimizer state, abandon first-order gradients, or change the update geometry while retaining dense state. The recently introduced Muon optimizer reduces optimizer memory through matrix-valued updates. Still, its geometry differs from AdamW and can lead to performance degradation when fine-tuning AdamW-pretrained models. To reduce optimizer memory without sacrificing accuracy or computational efficiency in LLM fine-tuning, we propose Ternary Absolute-max Column-wise One-sparse optimizer, or TACO, which follows Muon's operator-norm steepest-descent view but takes the geometric route further. TACO computes the exact steepest-descent direction under a dimension-normalized $1\to1$ operator norm by selecting the sign of the largest magnitude entry in each column of two-dimensional weight matrices. This retains first-order gradients while making optimizer state memory nearly negligible. Our practical TACO optimizer maintains only a small set of low precision gradient components per column, reducing persistent optimizer state by $174\times$ relative to AdamW8bit (from 27.7 GB to 0.16 GB) and peak training memory by $2.9\times$ (from 80.6 GB to 27.5 GB) on OPT-13B, while achieving comparable accuracy and runtime. TACO further enables full-parameter fine-tuning of 30-32B-parameter models on a single 80 GB H100 GPU across multiple model families and tasks.

cs.LG↗

arXiv2026

Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning

Step-size selection remains a central challenge in large-scale neural network optimization; conservative steps slow convergence, while aggressive steps can destabilize it. We combine \textbf{Z}ero-and-\textbf{F}irst-\textbf{O}rder optimization~(ZFO) and propose a lightweight framework that decouples direction selection from step-size. ZFO uses a trusted first-order optimizer to determine the direction and performs zeroth-order evaluations only along this one-dimensional subspace to choose how far to move. Using the current {gradient information} and two additional objective function evaluations, ZFO instances construct a local model of the objective function along the proposed direction and select a curvature-aware step within a bounded search interval. This yields an adaptive step-selection mechanism that costs less than a full line search. We provide theoretical guarantees to show that shared-sample evaluations produce reliable finite-difference curvature estimates, that the induced local model selects a near-optimal step along the search interval, and that ZFO converges to a neighborhood of a stationary point. Across the evaluated settings, language models and datasets, ZFO frequently improves optimization and final performance relative to fixed-step first-order baselines, with the magnitude and preferred local model depending on the objective. Our code is publicly available at: https://github.com/nizswan/Zeroth-First-Order-Framework.

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arXiv2026

Protein Representation Learning with Secondary-Structure and Energy-Filtered Hydrogen-Bond Graphs

Graph-based representations are widely used in protein modeling, yet many existing approaches rely primarily on sequence adjacency or geometric proximity, which only partially reflect the principles governing protein folding. Proteins instead adopt complex three-dimensional conformations organized around secondary structure elements, such as $α$-helices and $β$-sheets, which encode recurring local motifs and stabilizing hydrogen-bond interactions. In this work, we introduce a secondary-structure-aware graph neural network for protein representation learning. Residue-level node representations are augmented with secondary structure assignments, and graph edges are constructed from hydrogen-bond interactions filtered by their energetic strength. This design enables the model to capture both local structural context and long-range couplings that are central to protein stability and function. We evaluate the proposed approach on commonly used protein benchmarks and observe consistent improvements over existing graph-based methods. In addition, the resulting graph representations offer enhanced biological interpretability, as the learned connectivity aligns with established structural motifs. These findings suggest that incorporating secondary structure and energy-filtered hydrogen-bond topology provides an effective inductive bias for protein representation learning. The code is released at https://github.com/mohamedmohamed2021/SSProNet

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arXiv2026

Beyond LoRA: Is Sparsity-Induced Adaptation Better?

Low-rank adaptation (LoRA) and its variants provide a memory- and compute-efficient alternative to full fine-tuning of pre-trained models. However, questions remain about the comparative generalizability of these approaches and how the structural restrictions on low-rank updates preserve effective adaptation performance. We present a historical framing, covering the past (full fine-tuning and original LoRA), the present (different variants of LoRA), and propose simpler, cheaper, parameter-efficient extensions by inducing sparsity within existing LoRA variants: Cheap LoRA (cLA), training a single low-rank factor with the other fixed (deterministically or, in its randomized variant, stochastically), and the chained circulant variant, ${c}^3$LA. We frame cLA as a structured instance of asymmetric LoRA, serving as a controlled column-subspace restriction of full fine-tuning. We derive information-theoretic generalization error bounds for these variants, marking one of the first endeavors in this area. Empirically, we evaluate 11 fine-tuning methods across 10 pre-trained models and 14 datasets, analyzing the fine-tuned models' performance and generalization using tools such as loss landscapes and spectral analysis. Despite the sensitivity of fine-tuned models to the pre-trained model, datasets, and other factors, our study suggests that restricting LoRA-based PEFT methods' adaptation to a sparse, structured column space remains competitive across tasks with their parameter-matched baselines while reducing up to 10% training time and peak GPU memory up to 15%, even with a naïve, non-optimized, sparse implementation. Our theoretical and empirical generalization measures provide a more consistent and principled approach to their cost-effective adaptation than commonly used analytical tools. Overview and code are available at: https://elicaden.github.io/Beyond_LoRA/.

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arXiv2026

Direct-search methods for decentralized blackbox optimization

Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. In this paper, we adapt direct-search methods, a classical technique in derivative-free optimization, to the decentralized setting. In contrast with zeroth-order algorithms, our algorithms rely on positive spanning sets to define suitable search directions while still possessing global convergence guaranties, thanks to carefully chosen stepsizes. Numerical experiments highlight the advantages of direct-search techniques over gradient-approximation-based strategies.

math.OC↗

arXiv2026

Stabilizing Policy Gradient Methods via Reward Profiling

Policy gradient methods, which have been extensively studied in the last decade, offer an effective and efficient framework for reinforcement learning problems. However, their performances can often be unsatisfactory, suffering from unreliable reward improvements and slow convergence, due to high variance in gradient estimations. In this paper, we propose a universal reward profiling framework that can be seamlessly integrated with any policy gradient algorithm, where we selectively update the policy based on high-confidence performance estimations. We theoretically justify that our technique will not slow down the convergence of the baseline policy gradient methods, but with high probability, will result in stable and monotonic improvements of their performance. Empirically, on eight continuous-control benchmarks (Box2D and MuJoCo/PyBullet), our profiling yields up to 1.5x faster convergence to near-optimal returns, up to 1.75x reduction in return variance on some setups. Our profiling approach offers a general, theoretically grounded path to more reliable and efficient policy learning in complex environments.

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arXiv2025

FairEnergy: Contribution-Based Fairness meets Energy Efficiency in Federated Learning

Federated learning (FL) enables collaborative model training across distributed devices while preserving data privacy. However, balancing energy efficiency and fair participation while ensuring high model accuracy remains challenging in wireless edge systems due to heterogeneous resources, unequal client contributions, and limited communication capacity. To address these challenges, we propose FairEnergy, a fairness-aware energy minimization framework that integrates a contribution score capturing both the magnitude of updates and their compression ratio into the joint optimization of device selection, bandwidth allocation, and compression level. The resulting mixed-integer non-convex problem is solved by relaxing binary selection variables and applying Lagrangian decomposition to handle global bandwidth coupling, followed by per-device subproblem optimization. Experiments on non-IID data show that FairEnergy achieves higher accuracy while reducing energy consumption by up to 79\% compared to baseline strategies.

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arXiv2025

Just Few States are Enough: Randomized Sparse Feedback for Stability of Dynamical Systems

While classical control theory assumes that the controller has access to measurements of the entire state (or output) at every time instant, this paper investigates a setting where the feedback controller can only access a randomly selected subset of the state vector at each time step. Due to the random sparsification that selects only a subset of the state components at each step, we analyze the stability of the closed-loop system in terms of Asymptotic Mean-Square Stability (AMSS), which ensures that the system state converges to zero in the mean-square sense. We consider the problem of designing both a feedback gain matrix and a measurement sparsification strategy that minimizes the number of state components required for feedback, while ensuring AMSS of the closed-loop system. Interestingly, (1) we provide conditions on the dynamics of the system under which it is possible to find a sparsification strategy, and (2) we propose a Linear Matrix Inequality (LMI) based algorithm that jointly computes a stabilizing gain matrix, and a randomized sparsification strategy that minimizes the expected number of measured state coordinates while preserving the AMSS. Our approach is then extended to the case where the sparsification probabilities vary across the state components. Based on these theoretical findings, we propose an algorithmic procedure to compute the vector of sparsification parameters, along with the corresponding feedback gain matrix. To the best of our knowledge, this is the first study to investigate the stability properties of control systems that rely solely on randomly selected state measurements. Numerical simulations demonstrate that, in some settings, the system achieves comparable performance to full-state feedback while requiring measurements from only $0.3\%$ of the state coordinates.

eess.SY↗

arXiv2025

If You Want to Be Robust, Be Wary of Initialization

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a spectrum of graph-related tasks, however concerns persist regarding their vulnerability to adversarial perturbations. While prevailing defense strategies focus primarily on pre-processing techniques and adaptive message-passing schemes, this study delves into an under-explored dimension: the impact of weight initialization and associated hyper-parameters, such as training epochs, on a model's robustness. We introduce a theoretical framework bridging the connection between initialization strategies and a network's resilience to adversarial perturbations. Our analysis reveals a direct relationship between initial weights, number of training epochs and the model's vulnerability, offering new insights into adversarial robustness beyond conventional defense mechanisms. While our primary focus is on GNNs, we extend our theoretical framework, providing a general upper-bound applicable to Deep Neural Networks. Extensive experiments, spanning diverse models and real-world datasets subjected to various adversarial attacks, validate our findings. We illustrate that selecting appropriate initialization not only ensures performance on clean datasets but also enhances model robustness against adversarial perturbations, with observed gaps of up to 50\% compared to alternative initialization approaches.

cs.LG↗

arXiv2025

Where Have All the Kaczmarz Iterates Gone?

The randomized Kaczmarz (RK) algorithm is one of the most computationally and memory-efficient iterative algorithms for solving large-scale linear systems. However, practical applications often involve noisy and potentially inconsistent systems. While the convergence of RK is well understood for consistent systems, the study of RK on noisy, inconsistent linear systems is limited. This paper investigates the asymptotic behavior of RK iterates in expectation when solving noisy and inconsistent systems, addressing the locations of their limit points. We explore the roles of singular vectors of the (noisy) coefficient matrix and derive bounds on the convergence horizon, which depend on the noise levels and system characteristics. Finally, we provide extensive numerical experiments that validate our theoretical findings, offering practical insights into the algorithm's performance under realistic conditions. These results establish a deeper understanding of the RK algorithm's limitations and robustness in noisy environments, paving the way for optimized applications in real-world scientific and engineering problems.

math.NA↗

arXiv2025

AI-based identification and support of at-risk students: A case study of the Moroccan education system

Student dropout is a global issue influenced by personal, familial, and academic factors, with varying rates across countries. This paper introduces an AI-driven predictive modeling approach to identify students at risk of dropping out using advanced machine learning techniques. The goal is to enable timely interventions and improve educational outcomes. Our methodology is adaptable across different educational systems and levels. By employing a rigorous evaluation framework, we assess model performance and use Shapley Additive exPlanations (SHAP) to identify key factors influencing predictions. The approach was tested on real data provided by the Moroccan Ministry of National Education, achieving 88% accuracy, 88% recall, 86% precision, and an AUC of 87%. These results highlight the effectiveness of the AI models in identifying at-risk students. The framework is adaptable, incorporating historical data for both short and long-term detection, offering a comprehensive solution to the persistent challenge of student dropout.

cs.CY↗

arXiv2024

A Stochastic Iteratively Regularized Gauss-Newton Method

This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for infinite-dimensional problems. Recent work have extended this method to handle sequential observations, rather than a single instance of the data, demonstrating notable improvements in reconstruction accuracy. In this paper, we further extend these methods to a stochastic framework through mini-batching, introducing a new algorithm, the stochastic iteratively regularized Gauss-Newton method (SIRGNM). Our algorithm is designed through the use randomized sketching. We provide an analysis for the SIRGNM, which includes a preliminary error decomposition and a convergence analysis, related to the residuals. We provide numerical experiments on a 2D elliptic PDE example. This illustrates the effectiveness of the SIRGNM, through maintaining a similar level of accuracy while reducing on the computational time.

math.NA↗

arXiv2024

A Note on Randomized Kaczmarz Algorithm for Solving Doubly-Noisy Linear Systems

Large-scale linear systems, $Ax=b$, frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized Kaczmarz (RK) algorithm has been studied extensively as an efficient iterative solver for such systems. However, the convergence study of RK in the noisy regime is limited and considers measurement noise in the right-hand side vector, $b$. Unfortunately, in practice, that is not always the case; the coefficient matrix $A$ can also be noisy. In this paper, we analyze the convergence of RK for {\textit{doubly-noisy} linear systems, i.e., when the coefficient matrix, $A$, has additive or multiplicative noise, and $b$ is also noisy}. In our analyses, the quantity $\tilde R=\| \tilde A^{\dagger} \|^2 \|\tilde A \|_F^2$ influences the convergence of RK, where $\tilde A$ represents a noisy version of $A$. We claim that our analysis is robust and realistically applicable, as we do not require information about the noiseless coefficient matrix, $A$, and considering different conditions on noise, we can control the convergence of RK. {We perform numerical experiments to substantiate our theoretical findings.}

math.NA↗

arXiv2024

Energy Efficient Aerial RIS: Phase Shift Optimization and Trajectory Design

Reconfigurable Intelligent Surface (RIS) technology has gained significant attention due to its ability to enhance the performance of wireless communication systems. The main advantage of RIS is that it can be strategically placed in the environment to control wireless signals, enabling improvements in coverage, capacity, and energy efficiency. In this paper, we investigate a scenario in which a drone, equipped with a RIS, travels from an initial point to a target destination. In this scenario, the aerial RIS (ARIS) is deployed to establish a direct link between the base station and obstructed users. Our objective is to maximize the energy efficiency of the ARIS while taking into account its dynamic model including its velocity and acceleration along with the phase shift of the RIS. To this end, we formulate the energy efficiency problem under the constraints of the dynamic model of the drone. The studied problem is challenging to solve. To address this, we proceed as follows. First, we introduce an efficient solution that involves decoupling the phase shift optimization and the trajectory design. Specifically, the closed-form expression of the phase-shift is obtained using a convex approximation, which is subsequently integrated into the trajectory design problem. We then employ tools inspired by economic model predictive control (EMPC) to solve the resulting trajectory optimization. Our simulation results show a significant improvement in energy efficiency against the scenario where the dynamic model of the UAV is ignored.

eess.SP↗

arXiv2024

Semantic-Aware Resource Allocation in Constrained Networks with Limited User Participation

Semantic communication has gained attention as a key enabler for intelligent and context-aware communication. However, one of the key challenges of semantic communications is the need to tailor the resource allocation to meet the specific requirements of semantic transmission. In this paper, we focus on networks with limited resources where devices are constrained to transmit with limited bandwidth and power over large distance. Specifically, we devise an efficient strategy to select the most pertinent semantic features and participating users, taking into account the channel quality, the transmission time, and the recovery accuracy. To this end, we formulate an optimization problem with the goal of selecting the most relevant and accurate semantic features over devices while satisfying constraints on transmission time and quality of the channel. This involves optimizing communication resources, identifying participating users, and choosing specific semantic information for transmission. The underlying problem is inherently complex due to its non-convex nature and combinatorial constraints. To overcome this challenge, we efficiently approximate the optimal solution by solving a series of integer linear programming problems. Our numerical findings illustrate the effectiveness and efficiency of our approach in managing semantic communications in networks with limited resources.

cs.IT↗

arXiv2024

Joint Probability Selection and Power Allocation for Federated Learning

In this paper, we study the performance of federated learning over wireless networks, where devices with a limited energy budget train a machine learning model. The federated learning performance depends on the selection of the clients participating in the learning at each round. Most existing studies suggest deterministic approaches for the client selection, resulting in challenging optimization problems that are usually solved using heuristics, and therefore without guarantees on the quality of the final solution. We formulate a new probabilistic approach to jointly select clients and allocate power optimally so that the expected number of participating clients is maximized. To solve the problem, a new alternating algorithm is proposed, where at each step, the closed-form solutions for user selection probabilities and power allocations are obtained. Our numerical results show that the proposed approach achieves a significant performance in terms of energy consumption, completion time and accuracy as compared to the studied benchmarks.

cs.LG↗

arXiv2023

Age-of-Information in UAV-assisted Networks: a Decentralized Multi-Agent Optimization

Unmanned aerial vehicles (UAVs) are a highly promising technology with diverse applications in wireless networks. One of their primary uses is the collection of time-sensitive data from Internet of Things (IoT) devices. In UAV-assisted networks, the Age-of-Information (AoI) serves as a fundamental metric for quantifying data timeliness and freshness. In this work, we are interested in a generalized AoI formulation, where each packet's age is weighted based on its generation time. Our objective is to find the optimal UAVs' trajectories and the subsets of selected devices such that the weighted AoI is minimized. To address this challenge, we formulate the problem as a Mixed-Integer Nonlinear Programming (MINLP), incorporating time and quality of service constraints. To efficiently tackle this complex problem and minimize communication overhead among UAVs, we propose a distributed approach. This approach enables drones to make independent decisions based on locally acquired data. Specifically, we reformulate our problem such that our objective function is easily decomposed into individual rewards. The reformulated problem is solved using a distributed implementation of Multi-Agent Reinforcement Learning (MARL). Our empirical results show that the proposed decentralized approach achieves results that are nearly equivalent to a centralized implementation with a notable reduction in communication overhead.

math.OC↗

arXiv2023

Demystifying the Myths and Legends of Nonconvex Convergence of SGD

Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood, their convergence for nonconvex functions stands on weak mathematical foundations. Most existing studies on the nonconvex convergence of SGD show the complexity results based on either the minimum of the expected gradient norm or the functional sub-optimality gap (for functions with extra structural property) by searching the entire range of iterates. Hence the last iterations of SGDs do not necessarily maintain the same complexity guarantee. This paper shows that an $ε$-stationary point exists in the final iterates of SGDs, given a large enough total iteration budget, $T$, not just anywhere in the entire range of iterates -- a much stronger result than the existing one. Additionally, our analyses allow us to measure the density of the $ε$-stationary points in the final iterates of SGD, and we recover the classical $O(\frac{1}{\sqrt{T}})$ asymptotic rate under various existing assumptions on the objective function and the bounds on the stochastic gradient. As a result of our analyses, we addressed certain myths and legends related to the nonconvex convergence of SGD and posed some thought-provoking questions that could set new directions for research.

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