arXiv subjects

George Turkiyyah

Publications and source records attributed to George Turkiyyah.

At least 19 recordsLinked to original sources

arXiv2026

Whittle-Matérn Fields with Variable Smoothness

We introduce and analyze a nonlocal generalization of Whittle--Matérn Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\underline s,\overline s]\subset(0,1)$. The model is defined via an integral-form operator whose kernel is constructed from the modified Bessel function of the second kind and whose local singularity is governed by the symmetric exponent $β(x,y)=(s(x)+s(y))/2$. This variable-order nonlocal formulation departs from the classical constant-order pseudodifferential setting and raises new analytic and numerical challenges. We develop a novel variational framework adapted to the kernel, prove existence and uniqueness of weak solutions on truncated bounded domains, and derive Sobolev regularity of the Gaussian (spectral) solution controlled by the minimal local order, with realizations lying in $H^r(\mathcal G)$ for every $r<2\underline s-\tfrac{d}{2}$ with $d\ge2$ or $\underline s\le1/2$, with a slightly reduced range in the remaining case (i.e. $d=1$ and $\underline s > 1/2$), hence in $L_2(\mathcal G)$ when $\underline s>d/4$. Here $H^r(\mathcal G)$ denotes the Sobolev space on the bounded domain $\mathcal G$. We also present a finite-element sampling method for the integral model, derive error estimates, and provide numerical experiments in one dimension that illustrate the impact of spatially varying smoothness on the solution covariance. Computational aspects and directions for scalable implementations are discussed.

math.NA↗

arXiv2026

Turning the Spell Around: Lightweight Alignment Amplification via Rank-One Safety Injection

Safety alignment in Large Language Models (LLMs) often involves mediating internal representations to refuse harmful requests. Recent research has demonstrated that these safety mechanisms can be bypassed by ablating or removing specific representational directions within the model. In this paper, we propose the opposite approach: Rank-One Safety Injection (ROSI), a white-box method that amplifies a model's safety alignment by permanently steering its activations toward the refusal-mediating subspace. ROSI operates as a simple, fine-tuning-free rank-one weight modification applied to all residual stream write matrices. The required safety direction can be computed from a small set of harmful and harmless instruction pairs. We show that ROSI consistently increases safety refusal rates - as evaluated by Llama Guard 3 - while preserving the utility of the model on standard benchmarks such as MMLU, HellaSwag, and Arc. Furthermore, we show that ROSI can also re-align 'uncensored' models by amplifying their own latent safety directions, demonstrating its utility as an effective last-mile safety procedure. Our results suggest that targeted, interpretable weight steering is a cheap and potent mechanism to improve LLM safety, complementing more resource-intensive fine-tuning paradigms.

cs.CL↗

arXiv2026

Foundation Model-Assisted Full Waveform Inversion

Full waveform inversion (FWI) can recover high-resolution subsurface velocity models. Conventional waveform-difference objectives, however, are vulnerable to cycle skipping when the starting model is inaccurate. We introduce an FWI objective that compares features produced from modeled and observed seismic traces by SeisLM, a pretrained seismic foundation model. The SeisLM encoder remains frozen during inversion, and the feature discrepancy is differentiated with respect to the modeled traces to construct an adjoint source compatible with the standard adjoint-state framework. We also test a scheduled hybrid loss that combines the SeisLM feature loss with the conventional $L_2$ objective. Time-shift diagnostics show that the loss computed from features produced by the pretrained encoder has a broader and smoother basin around the correct alignment than either the waveform $L_2$ objective or the feature loss obtained from an encoder with the same architecture and randomly initialized parameters. In the Marmousi experiment, the SeisLM and hybrid objectives produce similar improvements during early-stage inversion and provide useful models for subsequent reflection-based $L_2$ refinement. In the 2D Overthrust experiment, which begins from a laterally invariant linear-gradient model, the SeisLM feature-loss workflow outperforms the conventional and hybrid workflows, indicating that introducing the $L_2$ contribution too early can reintroduce cycle-skipping sensitivity. In the 3D Overthrust experiment, conventional $L_2$ inversion stalls near the initial linear gradient, whereas the SeisLM feature loss guides the inversion toward a background model from which $L_2$ refinement recovers the principal structures. These results support using features produced by pretrained seismic networks to define early-stage FWI objectives rather than complete replacements for waveform-domain misfits.

physics.geo-ph↗

arXiv2026

Synthetic Geology: Structural Geology Meets Deep Learning

Reconstructing the structural geology and mineral composition of the first few kilometers of the Earth's subsurface from sparse or indirect surface observations remains a long-standing challenge with critical applications in mineral exploration, geohazard assessment, and geotechnical engineering. This inherently ill-posed problem is often addressed by classical geophysical inversion methods, which typically yield a single maximum-likelihood model that fails to capture the full range of plausible geology. The adoption of modern deep learning methods has been limited by the lack of large 3D training datasets. We address this gap with \textit{StructuralGeo}, a geological simulation engine that mimics eons of tectonic, magmatic, and sedimentary processes to generate a virtually limitless supply of realistic synthetic 3D lithological models. Using this dataset, we train both unconditional and conditional generative flow-matching models with a 3D attention U-Net architecture. The resulting foundation model can reconstruct multiple plausible 3D scenarios from surface topography and sparse borehole data, depicting structures such as layers, faults, folds, and dikes. By sampling many reconstructions from the same observations, we introduce a probabilistic framework for estimating the size and extent of subsurface features. While the realism of the output is bounded by the fidelity of the training data to true geology, this combination of simulation and generative AI functions offers a flexible prior for probabilistic modeling, regional fine-tuning, and use as an AI-based regularizer in traditional geophysical inversion workflows.

cs.CV↗

arXiv2025

A Deep Learning-based time shift objective function for Full Waveform Inversion

Full Waveform Inversion (FWI) is a powerful technique for estimating high-resolution subsurface velocity models by minimizing the discrepancy between modeled and observed seismic data. However, the oscillatory nature of seismic waveforms makes point-wise discrepancy measures highly prone to cycle-skipping, especially when the initial velocity model is inadequate. To address this challenge, various alternative misfit functions have been proposed in the literature, each with unique strengths and limitations. Dynamic Time Warping (DTW) is a popular technique in signal processing for aligning time series using dynamic programming. While a differentiable variant of DTW has been recently proposed, its use in FWI is hindered by high-frequency artifacts in the adjoint source and the substantial computational cost of gradient evaluations. In this study, we propose a neural network-based approach to learn the time shifts that align two time series in a supervised manner. The trained network is then utilized to compare traces from observed and modeled seismic data, offering a stable and computationally efficient alternative to DTW. Furthermore, the inherent differentiability of neural networks via backpropagation enables seamless integration into the FWI framework as a misfit function. We validate this approach on two synthetic datasets, namely the Marmousi model and the Chevron blind test dataset, demonstrating in both cases a similar convergence behavior to that of SoftDWT whilst drastically reducing the computational time of the adjoint source calculation.

physics.geo-ph↗

arXiv2025

An Embarrassingly Simple Defense Against LLM Abliteration Attacks

Large language models (LLMs) are typically aligned to refuse harmful instructions through safety fine-tuning. A recent attack, termed abliteration, identifies and suppresses the single latent direction most responsible for refusal behavior, thereby enabling models to generate harmful content. We propose a defense that fundamentally alters how models express refusal. We construct an extended-refusal dataset in which responses to harmful prompts provide detailed justifications before refusing, distributing the refusal signal across multiple token positions. Fine-tuning Llama-2-7B-Chat and Qwen2.5-Instruct (1.5B and 3B parameters) on this dataset yields models that maintain high refusal rates under abliteration: refusal rates drop by at most 10%, compared to 70-80% drops in baseline models. Comprehensive evaluations of safety and utility demonstrate that extended-refusal fine-tuning effectively neutralizes abliteration attacks while preserving general model performance and enhancing robustness across multiple alignment scenarios.

cs.CL↗

arXiv2025

ALARB: An Arabic Legal Argument Reasoning Benchmark

We introduce ALARB, a dataset and suite of tasks designed to evaluate the reasoning capabilities of large language models (LLMs) within the Arabic legal domain. While existing Arabic benchmarks cover some knowledge-intensive tasks such as retrieval and understanding, substantial datasets focusing specifically on multistep reasoning for Arabic LLMs, especially in open-ended contexts, are lacking. The dataset comprises over 13K commercial court cases from Saudi Arabia, with each case including the facts presented, the reasoning of the court, the verdict, as well as the cited clauses extracted from the regulatory documents. We define a set of challenging tasks leveraging this dataset and reflecting the complexity of real-world legal reasoning, including verdict prediction, completion of reasoning chains in multistep legal arguments, and identification of relevant regulations based on case facts. We benchmark a representative selection of current open and closed Arabic LLMs on these tasks and demonstrate the dataset's utility for instruction tuning. Notably, we show that instruction-tuning a modest 12B parameter model using ALARB significantly enhances its performance in verdict prediction and Arabic verdict generation, reaching a level comparable to that of GPT-4o.

cs.CL↗

arXiv2025

Linear Complexity $\mathcal{H}^2$ Direct Solver for Fine-Grained Parallel Architectures

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathcal{H}^2$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathcal{H}^2$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ``blackbox'' in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

cs.DC↗

arXiv2025

H2-MG: A multigrid method for hierarchical rank structured matrices

This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides the time and memory efficiency of H2 operator representation along with the rapid convergence of a multilevel method. We describe how H2-MG works, show its linear complexity, and demonstrate its effectiveness on two standard kernels and on a single-layer potential boundary element discretization with complex geometry. The current zoo of H2 solvers, which includes a wide variety of iterative and direct solvers, so far lacks a method that exploits multiple levels of resolution, commonly referred to in the iterative methods literature as ``multigrid'' from its origins in a hierarchy of grids used to discretize differential equations. This makes H2-MG a valuable addition to the collection of H2 solvers. The algorithm has potential for advancing various fields that require the solution of large, dense, symmetric positive definite matrices.

math.NA↗

arXiv2025

Cooperative Grasping for Collective Object Transport in Constrained Environments

We propose a novel framework for decision-making in cooperative grasping for two-robot object transport in constrained environments. The core of the framework is a Conditional Embedding (CE) model consisting of two neural networks that map grasp configuration information into an embedding space. The resulting embedding vectors are then used to identify feasible grasp configurations that allow two robots to collaboratively transport an object. To ensure generalizability across diverse environments and object geometries, the neural networks are trained on a dataset comprising a range of environment maps and object shapes. We employ a supervised learning approach with negative sampling to ensure that the learned embeddings effectively distinguish between feasible and infeasible grasp configurations. Evaluation results across a wide range of environments and objects in simulations demonstrate the model's ability to reliably identify feasible grasp configurations. We further validate the framework through experiments on a physical robotic platform, confirming its practical applicability.

cs.RO↗

arXiv2024

ArabLegalEval: A Multitask Benchmark for Assessing Arabic Legal Knowledge in Large Language Models

The rapid advancements in Large Language Models (LLMs) have led to significant improvements in various natural language processing tasks. However, the evaluation of LLMs' legal knowledge, particularly in non-English languages such as Arabic, remains under-explored. To address this gap, we introduce ArabLegalEval, a multitask benchmark dataset for assessing the Arabic legal knowledge of LLMs. Inspired by the MMLU and LegalBench datasets, ArabLegalEval consists of multiple tasks sourced from Saudi legal documents and synthesized questions. In this work, we aim to analyze the capabilities required to solve legal problems in Arabic and benchmark the performance of state-of-the-art LLMs. We explore the impact of in-context learning and investigate various evaluation methods. Additionally, we explore workflows for generating questions with automatic validation to enhance the dataset's quality. We benchmark multilingual and Arabic-centric LLMs, such as GPT-4 and Jais, respectively. We also share our methodology for creating the dataset and validation, which can be generalized to other domains. We hope to accelerate AI research in the Arabic Legal domain by releasing the ArabLegalEval dataset and code: https://github.com/Thiqah/ArabLegalEval

cs.CL↗

arXiv2024

PETScML: Second-order solvers for training regression problems in Scientific Machine Learning

In recent years, we have witnessed the emergence of scientific machine learning as a data-driven tool for the analysis, by means of deep-learning techniques, of data produced by computational science and engineering applications. At the core of these methods is the supervised training algorithm to learn the neural network realization, a highly non-convex optimization problem that is usually solved using stochastic gradient methods. However, distinct from deep-learning practice, scientific machine-learning training problems feature a much larger volume of smooth data and better characterizations of the empirical risk functions, which make them suited for conventional solvers for unconstrained optimization. We introduce a lightweight software framework built on top of the Portable and Extensible Toolkit for Scientific computation to bridge the gap between deep-learning software and conventional solvers for unconstrained minimization. We empirically demonstrate the superior efficacy of a trust region method based on the Gauss-Newton approximation of the Hessian in improving the generalization errors arising from regression tasks when learning surrogate models for a wide range of scientific machine-learning techniques and test cases. All the conventional second-order solvers tested, including L-BFGS and inexact Newton with line-search, compare favorably, either in terms of cost or accuracy, with the adaptive first-order methods used to validate the surrogate models.

cs.LG↗

arXiv2023

Finite element discretizations for variable-order fractional diffusion problems

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded domains. A number of challenges are encountered when discretizing these equations. The first comes from the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. An additional challenge comes from the need to handle volume conditions-the generalization of classical local boundary conditions to the nonlocal setting. Satisfying these conditions requires that the effect of the whole domain, including both the interior and exterior regions, can be computed on every interior point in the discretization. Performed directly, this would result in quadratic complexity. To address these challenges, we propose a strategy that decomposes the stiffness matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order. The second component handles the remaining smooth part of the near-field as well as the far field and is approximated by a hierarchical $\mathcal{H}^{2}$ matrix that maintains linear complexity in storage and operations. The third component handles the effect of the global mesh at every node and is written as a weighted mass matrix whose density is computed by a fast-multipole type method. The resulting algorithm has therefore overall linear space and time complexity. Analysis of the consistency of the stiffness matrix is provided and numerical experiments are conducted to illustrate the convergence and performance of the proposed algorithm.

math.NA↗

arXiv2021

H2Opus: A distributed-memory multi-GPU software package for non-local operators

Hierarchical $\mathcal{H}^2$-matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their $O(N)$ complexity in both memory and operator application makes them particularly suited for large-scale problems. As a result, there is a need for software that provides support for distributed operations on these matrices to allow large-scale problems to be represented. In this paper, we present high-performance, distributed-memory GPU-accelerated algorithms and implementations for matrix-vector multiplication and matrix recompression of hierarchical matrices in the $\mathcal{H}^2$ format. The algorithms are a new module of H2Opus, a performance-oriented package that supports a broad variety of $\mathcal{H}^2$-matrix operations on CPUs and GPUs. Performance in the distributed GPU setting is achieved by marshaling the tree data of the hierarchical matrix representation to allow batched kernels to be executed on the individual GPUs. MPI is used for inter-process communication. We optimize the communication data volume and hide much of the communication cost with local compute phases of the algorithms. Results show near-ideal scalability up to 1024 NVIDIA V100 GPUs on Summit, with performance exceeding 2.3 Tflop/s/GPU for the matrix-vector multiplication, and 670 Gflops/s/GPU for matrix compression, which involves batched QR and SVD operations. We illustrate the flexibility and efficiency of the library by solving a 2D variable diffusivity integral fractional diffusion problem with an algebraic multigrid-preconditioned Krylov solver and demonstrate scalability up to 16M degrees of freedom problems on 64 GPUs.

cs.DC↗

arXiv2021

Space-Fractional Diffusion with Variable Order and Diffusivity: Discretization and Direct Solution Strategies

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel singularity in the fractional integral operator and to the resulting dense discretized operators, which quickly become prohibitively expensive to handle because of their memory and arithmetic complexities. In this work, we present a singularity-aware discretization scheme that regularizes the singular integrals through a singularity subtraction technique adapted to the spatial variability of diffusivity and fractional order. This regularization strategy is conveniently formulated as a sparse matrix correction that is added to the dense operator, and is applicable to different formulations of fractional diffusion equations. We also present a block low rank representation to handle the dense matrix representations, by exploiting the ability to approximate blocks of the resulting formally dense matrix by low rank factorizations. A Cholesky factorization solver operates directly on this representation using the low rank blocks as its atomic computational tiles, and achieves high performance on multicore hardware. Numerical results show that the singularity treatment is robust, substantially reduces discretization errors, and attains the first-order convergence rate allowed by the regularity of the solutions. They also show that considerable savings are obtained in storage ($O(N^{1.5})$) and computational cost ($O(N^2)$) compared to dense factorizations. This translates to orders-of-magnitude savings in memory and time on multi-dimensional problems, and shows that the proposed methods offer practical tools for tackling large nonlocal fractional diffusion simulations.

math.NA↗

arXiv2021

H2OPUS-TLR: High Performance Tile Low Rank Symmetric Factorizations using Adaptive Randomized Approximation

Tile low rank representations of dense matrices partition them into blocks of roughly uniform size, where each off-diagonal tile is compressed and stored as its own low rank factorization. They offer an attractive representation for many data-sparse dense operators that appear in practical applications, where substantial compression and a much smaller memory footprint can be achieved. TLR matrices are a compromise between the simplicity of a regular perfectly-strided data structure and the optimal complexity of the unbalanced trees of hierarchically low rank matrices, and provide a convenient performance-tuning parameter through their tile size that can be proportioned to take into account the cache size where the tiles reside in the memory hierarchy. There are currently no high-performance algorithms that can generate Cholesky and $LDL^T$ factorizations, particularly on GPUs. The difficulties in achieving high performance when factoring TLR matrices come from the expensive compression operations that must be performed during the factorization process and the adaptive rank distribution of the tiles that causes an irregular work pattern for the processing cores. In this work, we develop a dynamic batching operation and combine it with batched adaptive randomized approximations to achieve high performance both on GPUs and CPUs. Our implementation attains over 1.2 TFLOP/s in double precision on the V100 GPU, and is limited by the performance of batched GEMM operations. The Cholesky factorization of covariance matrix of size $N = 131K$ arising in spatial statistics can be factored to an accuracy $ε=10^{-2}$ in just a few seconds. We believe the proposed GEMM-centric algorithm allows it to be readily ported to newer hardware such as the tensor cores that are optimized for small GEMM operations.

cs.DC↗

arXiv2020

Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs

Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as well as Markov chain Monte Carlo sampling of posteriors in the Bayesian setting. These methods require the ability to repeatedly perform such operations on the Hessian as multiplication with arbitrary vectors, solving linear systems, inversion, and (inverse) square root. Unfortunately, the Hessian is a (formally) dense, implicitly-defined operator that is intractable to form explicitly for practical inverse problems, requiring as many PDE solves as inversion parameters. Low rank approximations are effective when the data contain limited information about the parameters, but become prohibitive as the data become more informative. However, the Hessians for many inverse problems arising in practical applications can be well approximated by matrices that have hierarchically low rank structure. Hierarchical matrix representations promise to overcome the high complexity of dense representations and provide effective data structures and matrix operations that have only log-linear complexity. In this work, we describe algorithms for constructing and updating hierarchical matrix approximations of Hessians, and illustrate them on a number of representative inverse problems involving time-dependent diffusion, advection-dominated transport, frequency domain acoustic wave propagation, and low frequency Maxwell equations, demonstrating up to an order of magnitude speedup compared to globally low rank approximations.

math.NA↗

arXiv2019

Hierarchical Matrix Operations on GPUs: Matrix-Vector Multiplication and Compression

Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces representations that can be stored and operated on in near-linear complexity instead of the usual polynomial complexity of dense matrices. In this paper, we present high performance implementations of matrix vector multiplication and compression operations for the $\mathcal{H}^2$ variant of hierarchical matrices on GPUs. This variant exploits, in addition to the hierarchical block partitioning, hierarchical bases for the block representations and results in a scheme that requires only $O(n)$ storage and $O(n)$ complexity for the mat-vec and compression kernels. These two operations are at the core of algebraic operations for hierarchical matrices, the mat-vec being a ubiquitous operation in numerical algorithms while compression/recompression represents a key building block for other algebraic operations, which require periodic recompression during execution. The difficulties in developing efficient GPU algorithms come primarily from the irregular tree data structures that underlie the hierarchical representations, and the key to performance is to recast the computations on flattened trees in ways that allow batched linear algebra operations to be performed. This requires marshaling the irregularly laid out data in a way that allows them to be used by the batched routines. Marshaling operations only involve pointer arithmetic with no data movement and as a result have minimal overhead. Our numerical results on covariance matrices from 2D and 3D problems from spatial statistics show the high efficiency our routines achieve---over 550GB/s for the bandwidth-limited mat-vec and over 850GFLOPS/s in sustained performance for the compression on the P100 Pascal GPU.

cs.DS↗