arXiv subjects

Ahmed Abdelkader

Publications and source records attributed to Ahmed Abdelkader.

18 recordsLinked to original sources

arXiv2026

Differentiable Approximations for Distance Queries

The widespread use of gradient-based optimization has motivated the adaptation of various classical algorithms into differentiable solvers compatible with learning pipelines. In this paper, we investigate the enhancement of traditional geometric query problems such that the result consists of both the geometric function as well as its gradient. Specifically, we study the fundamental problem of distance queries against a set of points $P$ in $\mathbb{R}^d$, which also underlies various similarity measures for learning algorithms. The main result of this paper is a multiplicative $(1+\varepsilon)$-approximation of the Euclidean distance to $P$ which is differentiable at all points in $\mathbb{R}^d \setminus P$ with asymptotically optimal bounds on the norms of its gradient and Hessian, from a data structure with storage and query time matching state-of-the-art results for approximate nearest-neighbor searching. The approximation is realized as a regularized distance through a partition-of-unity framework, which efficiently blends multiple local approximations, over a suitably defined covering of space, into a smooth global approximation. In order to obtain the local distance approximations in a manner that facilitates blending, we develop a new approximate Voronoi diagram based on a simple point-location data structure, simplifying away both the lifting transformation and ray shooting.

cs.CG↗

arXiv2026

Mining Attribute Subspaces for Efficient Fine-tuning of 3D Foundation Models

With the emergence of 3D foundation models, there is growing interest in fine-tuning them for downstream tasks, where LoRA is the dominant fine-tuning paradigm. As 3D datasets exhibit distinct variations in texture, geometry, camera motion, and lighting, there are interesting fundamental questions: 1) Are there LoRA subspaces associated with each type of variation? 2) Are these subspaces disentangled (i.e., orthogonal to each other)? 3) How do we compute them effectively? This paper provides answers to all these questions. We introduce a robust approach that generates synthetic datasets with controlled variations, fine-tunes a LoRA adapter on each dataset, and extracts a LoRA sub-space associated with each type of variation. We show that these subspaces are approximately disentangled. Integrating them leads to a reduced LoRA subspace that enables efficient LoRA fine-tuning with improved prediction accuracy for downstream tasks. In particular, we show that such a reduced LoRA subspace, despite being derived entirely from synthetic data, generalizes to real datasets. An ablation study validates the effectiveness of the choices in our approach.

cs.CV↗

arXiv2026

Mull-Tokens: Modality-Agnostic Latent Thinking

Reasoning goes beyond language; the real world requires reasoning about space, time, affordances, and much more that words alone cannot convey. Existing multimodal models exploring the potential of reasoning with images are brittle and do not scale. They rely on calling specialist tools, costly generation of images, or handcrafted reasoning data to switch between text and image thoughts. Instead, we offer a simpler alternative -- Mull-Tokens -- modality-agnostic latent tokens pre-trained to hold intermediate information in either image or text modalities to let the model think free-form towards the correct answer. We investigate best practices to train Mull-Tokens inspired by latent reasoning frameworks. We first train Mull-Tokens using supervision from interleaved text-image traces, and then fine-tune without any supervision by only using the final answers. Across four challenging spatial reasoning benchmarks involving tasks such as solving puzzles and taking different perspectives, we demonstrate that Mull-Tokens improve upon several baselines utilizing text-only reasoning or interleaved image-text reasoning, achieving a +3% average improvement and up to +16% on a puzzle solving reasoning-heavy split compared to our strongest baseline. Adding to conversations around challenges in grounding textual and visual reasoning, Mull-Tokens offers a simple solution to abstractly think in multiple modalities.

cs.CV↗

arXiv2026

Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates

Structure-from-Motion (SfM) is a fundamental 3D vision task for recovering camera parameters and scene geometry from multi-view images. While recent deep learning advances enable accurate Monocular Depth Estimation (MDE) from single images without depending on camera motion, integrating MDE into SfM remains a challenge. Unlike conventional triangulated sparse point clouds, MDE produces dense depth maps with significantly higher error variance. Inspired by modern RANSAC estimators, we propose Marginalized Bundle Adjustment (MBA) to mitigate MDE error variance leveraging its density. With MBA, we show that MDE depth maps are sufficiently accurate to yield SoTA or competitive results in SfM and camera relocalization tasks. Through extensive evaluations, we demonstrate consistently robust performance across varying scales, ranging from few-frame setups to large multi-view systems with thousands of images. Our method highlights the significant potential of MDE in multi-view 3D vision.

cs.CV↗

arXiv2026

Adversarial Vulnerability Transcends Computational Paradigms: Feature Engineering Provides No Defense Against Neural Adversarial Transfer

Deep neural networks are vulnerable to adversarial examples--inputs with imperceptible perturbations causing misclassification. While adversarial transfer within neural networks is well-documented, whether classical ML pipelines using handcrafted features inherit this vulnerability when attacked via neural surrogates remains unexplored. Feature engineering creates information bottlenecks through gradient quantization and spatial binning, potentially filtering high-frequency adversarial signals. We evaluate this hypothesis through the first comprehensive study of adversarial transfer from DNNs to HOG-based classifiers. Using VGG16 as a surrogate, we generate FGSM and PGD adversarial examples and test transfer to four classical classifiers (KNN, Decision Tree, Linear SVM, Kernel SVM) and a shallow neural network across eight HOG configurations on CIFAR-10. Our results strongly refute the protective hypothesis: all classifiers suffer 16.6%-59.1% relative accuracy drops, comparable to neural-to-neural transfer. More surprisingly, we discover attack hierarchy reversal--contrary to patterns where iterative PGD dominates FGSM within neural networks, FGSM causes greater degradation than PGD in 100% of classical ML cases, suggesting iterative attacks overfit to surrogate-specific features that don't survive feature extraction. Block normalization provides partial but insufficient mitigation. These findings demonstrate that adversarial vulnerability is not an artifact of end-to-end differentiability but a fundamental property of image classification systems, with implications for security-critical deployments across computational paradigms.

cs.LG↗

arXiv2024

Graph Analysis of Citation and Co-authorship Networks of Egyptian Authors

The current research conducts a comprehensive analysis of citation networks focusing on publications by authors affiliated with Egyptian institutions. Leveraging the Semantic Scholar platform and its API, a citation network and a co-authorship network graphs are constructed to visualize the interconnections among these publications and their authors. This is done using the Python package for graph analysis (Networkx). The primary objective is to identify influential Egyptian publications and assess the centrality of nodes within the citation network. Through meticulous data collection including web scraping techniques, we obtained a cleaned dataset comprising publications by authors affiliated with Egyptian institutions. The analysis addresses challenges related to data quality, technical intricacies, and time constraints, resulting in a reliable and robust dataset. The findings provide valuable information on the impact of Egyptian publications, offering insights into the scholarly influence of authors associated with Egyptian institutions. This research equips researchers and academics interested in evaluating the impact of Egyptian publications with valuable data for future studies, collaborations, and policy decisions.

cs.DL↗

arXiv2023

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.

cs.GR↗

arXiv2023

Linear-Sized Spectral Sparsifiers and the Kadison-Singer Problem

The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava (MSS) [Ann. Math. 182, 327-350 (2015)], has been informally thought of as a strengthening of Batson, Spielman, and Srivastava's theorem that every undirected graph has a linear-sized spectral sparsifier [SICOMP 41, 1704-1721 (2012)]. We formalize this intuition by using a corollary of the MSS result to derive the existence of spectral sparsifiers with a number of edges linear in their number of vertices for all undirected, weighted graphs. The proof consists of two steps. First, following a suggestion of Srivastava [Asia Pac. Math. Newsl. 3, 15-20 (2013)], we show the result in the special case of graphs with bounded leverage scores by repeatedly applying the MSS corollary to partition the graph, while maintaining an appropriate bound on the leverage scores of each subgraph. Then, we extend to the general case by constructing a recursive algorithm that repeatedly (i) divides edges with high leverage scores into multiple parallel edges and (ii) uses the bounded leverage score case to sparsify the resulting graph.

cs.DS↗

arXiv2023

Smooth Distance Approximation

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously. In many real-world applications of geometric data structures, it is assumed that query results are continuous, free of jump discontinuities. This is at odds with many modern data structures in computational geometry, which employ approximations to achieve efficiency, but these approximations often suffer from discontinuities. In this paper, we present a general method for transforming an approximate but discontinuous data structure into one that produces a smooth approximation, while matching the asymptotic space efficiencies of the original. We achieve this by adapting an approach called the partition-of-unity method, which smoothly blends multiple local approximations into a single smooth global approximation. We illustrate the use of this technique in a specific application of approximating the distance to the boundary of a convex polytope in $\mathbb{R}^d$ from any point in its interior. We begin by developing a novel data structure that efficiently computes an absolute $\varepsilon$-approximation to this query in time $O(\log (1/\varepsilon))$ using $O(1/\varepsilon^{d/2})$ storage space. Then, we proceed to apply the proposed partition-of-unity blending to guarantee the smoothness of the approximate distance field, establishing optimal asymptotic bounds on the norms of its gradient and Hessian.

cs.CG↗

arXiv2023

Approximate Nearest Neighbor Searching with Non-Euclidean and Weighted Distances

We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a distance function that satisfies certain smoothness and growth-rate assumptions. The objective is to preprocess $S$ into a data structure so that for any query point $q$ in $\mathbb{R}^d$, it is possible to efficiently report any point of $S$ whose distance from $q$ is within a factor of $1+\varepsilon$ of the actual closest point. Prior to this work, the most efficient data structures for approximate nearest-neighbor searching in spaces of constant dimensionality applied only to the Euclidean metric. This paper overcomes this limitation through a method called convexification. For admissible distance functions, the proposed data structures answer queries in logarithmic time using $O(n \log (1 / \varepsilon) / \varepsilon^{d/2})$ space, nearly matching the best known bounds for the Euclidean metric. These results apply to both convex scaling distance functions (including the Mahalanobis distance and weighted Minkowski metrics) and Bregman divergences (including the Kullback-Leibler divergence and the Itakura-Saito distance).

cs.CG↗

arXiv2022

Detection as Regression: Certified Object Detection by Median Smoothing

Despite the vulnerability of object detectors to adversarial attacks, very few defenses are known to date. While adversarial training can improve the empirical robustness of image classifiers, a direct extension to object detection is very expensive. This work is motivated by recent progress on certified classification by randomized smoothing. We start by presenting a reduction from object detection to a regression problem. Then, to enable certified regression, where standard mean smoothing fails, we propose median smoothing, which is of independent interest. We obtain the first model-agnostic, training-free, and certified defense for object detection against $\ell_2$-bounded attacks. The code for all experiments in the paper is available at http://github.com/Ping-C/CertifiedObjectDetection .

cs.CV↗

arXiv2021

The Intrinsic Dimension of Images and Its Impact on Learning

It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations. This idea underlies a common intuition for the remarkable success of deep learning in computer vision. In this work, we apply dimension estimation tools to popular datasets and investigate the role of low-dimensional structure in deep learning. We find that common natural image datasets indeed have very low intrinsic dimension relative to the high number of pixels in the images. Additionally, we find that low dimensional datasets are easier for neural networks to learn, and models solving these tasks generalize better from training to test data. Along the way, we develop a technique for validating our dimension estimation tools on synthetic data generated by GANs allowing us to actively manipulate the intrinsic dimension by controlling the image generation process. Code for our experiments may be found here https://github.com/ppope/dimensions.

cs.CV↗

arXiv2021

Approximate Nearest-Neighbor Search for Line Segments

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider nearest-neighbor queries against a set of line segments in $\mathbb{R}^d$, for constant dimension $d$. Given a set $S$ of $n$ disjoint line segments in $\mathbb{R}^d$ and an error parameter $\varepsilon > 0$, the objective is to build a data structure such that for any query point $q$, it is possible to return a line segment whose Euclidean distance from $q$ is at most $(1+\varepsilon)$ times the distance from $q$ to its nearest line segment. We present a data structure for this problem with storage $O((n^2/\varepsilon^{d}) \log (Δ/\varepsilon))$ and query time $O(\log (\max(n,Δ)/\varepsilon))$, where $Δ$ is the spread of the set of segments $S$. Our approach is based on a covering of space by anisotropic elements, which align themselves according to the orientations of nearby segments.

cs.CG↗

arXiv2020

Certified Defenses for Adversarial Patches

Adversarial patch attacks are among one of the most practical threat models against real-world computer vision systems. This paper studies certified and empirical defenses against patch attacks. We begin with a set of experiments showing that most existing defenses, which work by pre-processing input images to mitigate adversarial patches, are easily broken by simple white-box adversaries. Motivated by this finding, we propose the first certified defense against patch attacks, and propose faster methods for its training. Furthermore, we experiment with different patch shapes for testing, obtaining surprisingly good robustness transfer across shapes, and present preliminary results on certified defense against sparse attacks. Our complete implementation can be found on: https://github.com/Ping-C/certifiedpatchdefense.

cs.CR↗

arXiv2020

Headless Horseman: Adversarial Attacks on Transfer Learning Models

Transfer learning facilitates the training of task-specific classifiers using pre-trained models as feature extractors. We present a family of transferable adversarial attacks against such classifiers, generated without access to the classification head; we call these \emph{headless attacks}. We first demonstrate successful transfer attacks against a victim network using \textit{only} its feature extractor. This motivates the introduction of a label-blind adversarial attack. This transfer attack method does not require any information about the class-label space of the victim. Our attack lowers the accuracy of a ResNet18 trained on CIFAR10 by over 40\%.

cs.LG↗

arXiv2018

On Realistic Target Coverage by Autonomous Drones

Low-cost mini-drones with advanced sensing and maneuverability enable a new class of intelligent sensing systems. To achieve the full potential of such drones, it is necessary to develop new enhanced formulations of both common and emerging sensing scenarios. Namely, several fundamental challenges in visual sensing remain unsolved including: 1) Fitting sizable targets in camera frames; 2) Effective viewpoints matching target poses; 3) Occlusion by elements in the environment, including other targets. In this paper, we introduce Argus: an autonomous system that utilizes drones to incrementally collect target information through a two-tier architecture. To tackle the stated challenges, Argus employs a novel geometric model that captures both target shapes and coverage constraints. Recognizing drones as the scarcest resource, Argus aims to minimize the number of drones required to cover a set of targets. We prove this problem is NP-hard, and even hard to approximate, before deriving a best-possible approximation algorithm along with a competitive sampling heuristic which runs up to 100x faster according to large-scale simulations. To test Argus in action, we demonstrate and analyze its performance on a prototype implementation. Finally, we present a number of extensions to accommodate more application requirements and highlight some open problems.

cs.RO↗

arXiv2018

Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from $α$-shapes and the power crust algorithm to produce unweighted Voronoi cells conforming to the surface, yielding the first provably-correct algorithm for this problem. Given an $ε$-sample on the bounding surface, with a weak $σ$-sparsity condition, we work with the balls of radius $δ$ times the local feature size centered at each sample. The corners of this union of balls are the Voronoi sites, on both sides of the surface. The facets common to cells on opposite sides reconstruct the surface. For appropriate values of $ε$, $σ$ and $δ$, we prove that the surface reconstruction is isotopic to the bounding surface. With the surface protected, the enclosed volume can be further decomposed into an isotopic volume mesh of fat Voronoi cells by generating a bounded number of sites in its interior. Compared to state-of-the-art methods based on clipping, VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees. Compared to the power crust algorithm, VoroCrust cells are not filtered, are unweighted, and offer greater flexibility in meshing the enclosed volume by either structured grids or random samples.

cs.CG↗

arXiv2015

On the Complexity of Slide-and-Merge Games

We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide all rows or columns of the board in one direction to create a high value tile by merging pairs of equal tiles into one with the sum of their values. This combines features from both block pushing and tile matching puzzles, like Push and Bejeweled, respectively. We define a number of natural decision problems on a suitable generalization of these games and prove NP-hardness for 2048 by reducing from 3SAT. Finally, we discuss the adaptation of our reduction to Threes and conjecture a similar result.

cs.CC↗