arXiv subjects

Hassan Ugail

Publications and source records attributed to Hassan Ugail.

At least 19 recordsLinked to original sources

arXiv2026

Proximity-Preserving Neural Subdivision

Classical subdivision schemes are widely used because they are local, repeatable, and analytically tractable. A single stencil defines the entire refinement rule, and the behaviour of the resulting operator under iteration is well understood. This uniformity, however, means that fixed stencils tend to underfit localised geometric features, such as sharp ridges or soft edges, where curvature is concentrated. Neural mesh refinement can adapt to such features, yet unconstrained vertex prediction usually lacks the structural behaviour required of a subdivision operator once the refinement rule is applied to its own output. In this work, we introduce Proximity-Preserving Neural Subdivision, or PNS for short. PNS is a trainable refinement rule that augments Loop subdivision with a small, bounded, curvature-gated correction expressed in a covariant local frame. The construction is designed so that, for any finite network weights, the operator is exactly equivariant under rigid motion, reproduces planar input exactly, and remains inside a quadratic proximity envelope around the Loop stencil. At planar valence-k stars, the linearised operator agrees with Loop, and it therefore inherits Loop's tangent eigenspaces and Reif spectral gap at that reference configuration. All of these properties are architectural and hold before any training takes place. Empirically, PNS improves the approximation of localised ridge features while remaining inside its prescribed proximity envelope under repeated subdivision. An unconstrained neural baseline, in contrast, achieves stronger one-step fitting but develops high-frequency artefacts and leaves the subdivision regime once iterated. The overall message of this work is that learning can be introduced into subdivision without abandoning the structural constraints that make subdivision useful as a geometry-processing primitive.

cs.GR↗

arXiv2026

A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognition

Online handwriting recognition systems typically represent pen trajectories through fixed-length Euclidean shape descriptors that capture the spatial outline of each stroke, but are insensitive to the order in which that outline is produced. Two strokes that trace the same region of the plane in opposite directions are indistinguishable to any such order-blind representation, yet their traversal directions may carry decisive class information in characters where loop orientation and stroke sequencing matter. This paper introduces a Heisenberg-lift framework that addresses this gap through a compact, interpretable, order-sensitive augmentation for online pen-trajectory features. The simplest instance is the terminal signed area, a single parameter-free scalar appended to an existing Euclidean descriptor at negligible computational cost. Evaluated on two standard online handwriting benchmarks, this one-scalar addition, consistently raises classifier accuracy over the Euclidean baseline. On the hardest character pair in our study, the letters o and y, the signed area alone achieves perfect separation while the Euclidean baseline falls short. The advantage grows further under additive coordinate noise, a practically relevant degradation in pen-trajectory data. A richer fifteen-dimensional extension, derived from a noncommutative Heisenberg-group subdivision scheme, provides additional gains in noisy and loop-structured conditions. Dimension-matched statistical controls confirm that all improvements reflect geometric information rather than feature-count inflation. The resulting descriptor is lightweight, closed-form, and directly interpretable, making it a practical augmentation for online handwriting and related document-trajectory classification pipelines in which the direction of stroke execution carries discriminative information.

cs.CV↗

arXiv2026

Adaptive Interpolatory Curve Subdivision with Learned Local Angles

Curve subdivision is pivotal in computer graphics for generating smooth geometric objects from control polygons. Interpolatory subdivision is especially attractive because the refined curve is guaranteed to pass through the designer's control points. Classical four-point and six-point schemes preserve this property, but their behaviour is governed by a single global tension parameter, limiting their ability to adapt across flat regions, sharp turns and varying local geometries. We introduce an adaptive local-angle formulation that keeps the interpolatory structure intact while learning how each new vertex should be inserted. A compact edge-wise predictor assigns one insertion angle per edge, while the original vertices are copied exactly at every refinement level. Interpolation is therefore a structural property of the operator and does not depend on the trained weights. The same predictor is used with geometry-specific geodesic primitives on the Euclidean plane, the two-sphere and the Poincaré disk. Under a matched-density evaluation protocol, the method reduces nearest-neighbour error by factors of five to seventeen over the best validation-tuned fixed-tension baseline, and by about 1.8 over centripetal Catmull-Rom in the Euclidean case. It also substantially reduces bending energy and tangent roughness, while remaining competitive with separately trained per-geometry models.

cs.CV↗

arXiv2026

Reliable Weyl Diagnostics for an Inhomogeneous Universe in Numerical Relativity

The electric and magnetic parts of the Weyl tensor provide a geometric diagnostic for describing the local gravitational structure of an inhomogeneous universe, and they allow us to distinguish tidal, gravitomagnetic, radiative, and silent regimes. However, when these diagnostics are computed from numerical relativity data, their interpretation depends on how well the data satisfy the Einstein constraint equations. A small constraint error can create a spurious magnetic signal, especially near a silent regime, and it may therefore be mistaken for genuine radiative structure. In this work, we treat the Hamiltonian and momentum constraint residuals as reliability gates for the Weyl diagnostics. Rather than imposing a fixed tolerance, we measure how a constraint error affects the corresponding Weyl classification, and we then calibrate the tolerance required to achieve a chosen accuracy. Our noise-induced synthetic tests show that the Hamiltonian residual determines the reliability of the electric Weyl diagnostic, whereas the momentum residual determines the reliability of the magnetic Weyl diagnostic. Furthermore, a real numerical relativity initial-data slice confirms that no universal tolerance is adequate. Thus, the calibration measures the slice-level sensitivity of the diagnostics rather than the truncation error of an evolution.

physics.gen-ph↗

arXiv2026

A Heisenberg Subdivision Scheme with Central Smoothness Loss

We introduce an interpolatory subdivision scheme for control polygons that take values in the three-dimensional Heisenberg group, the simplest noncommutative model geometry. The scheme keeps existing points at every refinement step and inserts new ones by a coordinate rule whose central correction comes from the group law. The two horizontal coordinates are refined by the classical four-point scheme of Dyn, Gregory and Levin, while the central coordinate acquires a closed-form correction built from a signed area of neighbouring horizontal data. Our main finding concerns the regularity of the limit curve. The horizontal part is exactly the classical four-point limit and inherits its smoothness. The central part behaves very differently. We prove that it converges to a continuous limit that belongs to the Zygmund class, with a logarithmic modulus of continuity. Under an explicit and verifiable condition on the central forcing, this logarithmic bound is sharp, because the scaled first differences then grow linearly with the refinement level, and the limit fails to be continuously differentiable. The effect is confirmed numerically. The correction is harmless at any single refinement step, but its repeated injection at every scale is what impacts smoothness. The example serves as a caution for nonlinear and group-valued subdivision, where a geometrically natural correction can impact regularity.

math.NA↗

arXiv2026

Symmetry-Structured Neural Completion of Islamic Geometric Patterns from Sparse Control Geometry

Islamic geometric patterns are governed by exact rotational symmetry and strict construction rules. This paper treats these rules as formal geometric knowledge and embeds them in a neural completion framework, rather than leaving them to be learned statistically from data. Given sparse control geometry and a target symmetry order, the system completes the pattern as a vector graph by predicting edges and refinements of bounded curves over a candidate lattice whose edges are organised into rotational orbits under the cyclic group. Symmetry is enforced either by constraining predictions within these orbits or by projecting them onto them during inference. The orbit-tied variant provides a constructive guarantee: for any input and any orbit-level selection rule, it produces exact N-fold symmetry, preserves anchor points, and keeps all refinements within prescribed bounds. These properties are verified numerically. The study focuses on rotational symmetry, and all quantitative results are obtained from procedurally generated graphs inspired by Islamic geometric design rather than from a historical corpus. On clean inputs, enforcing exact validity produces no measurable loss in fidelity. When control geometry is missing, an unstructured decoder loses fidelity and breaks symmetry; retraining on corrupted inputs recovers much of the fidelity but not exact validity. Symmetry-structured inference, by contrast, keeps violations at zero throughout. The results show that augmentation and symmetry structure address distinct failure modes: augmentation improves fidelity under corruption, while symmetry structure guarantees validity. The framework therefore provides a knowledge-constrained, guarantee-backed approach to neural completion for scalable vector ornaments whose validity depends on exact geometric structure.

cs.CV↗

arXiv2026

A Coherence Law for Trainability in Noisy Equivariant Quantum Neural Networks

Symmetry provides a quantum neural network structure, but on its own it does not keep the network trainable once noise is present. We ask which physical quantity decides whether the gradients of an equivariant circuit survive decoherence, and we answer with a compact training law. Working with U(1)-equivariant brickwork circuits that conserve a charge, we find that two distinct effects govern a trainable gradient. Causality fixes where the gradient can live, confining it to the backward light cone of the readout inside the active charge sector. Coherence then determines how fast it decays through the contraction of the off-diagonal sector modes that the projected readout can actually observe. We prove a light-cone reduction that pins the noiseless gradient to the sector-restricted cone with a lower bound independent of the total qubit number, and we define a readout-visible aligned coherence rate as a Rayleigh quotient of the noise generator along the gradient-carrying mode. A perturbative open-system analysis turns this rate into a leading-order training law. Density-matrix simulations then confirm that the finite-noise degradation follows a single accumulated variable built from noise depth and coherence contraction, with a coefficient of determination of 0.979. The sharpest test comes from a correlated-dephasing channel that has a large worst-case rate but a near-zero aligned rate. The law predicts no gradient loss for this channel, and none is seen. Sector coherence outperforms every standard channel diagnostic we compare it against, and the analysis identifies readout-visible sector coherence as the quantity that links equivariant architecture, open-system dynamics and noisy trainability.

quant-ph↗

arXiv2026

Geometric Phase-Space Structure in Cosmological Solutions of Einstein's Field Equations

Einstein field equations allow cosmological dynamics to depart from the Friedmann-Lemaitre-Robertson-Walker (FLRW) idealisation in several physically different ways. Matter may become spatially inhomogeneous, the local expansion scalar may vary across a hypersurface, the expansion may acquire anisotropic components through shear, and the free gravitational field may be encoded in nonzero Weyl curvature. The key question is not only how far a model is from FLRW, but which geometric mechanism is responsible. A single departure from FLRW number cannot distinguish these mechanisms. This paper introduces a compact geometric diagnostic framework that keeps them separate while using standard quantities in general relativity. The framework is observer-explicit and domain-explicit, intended as a practical tool for comparing analytic and numerical solution families rather than as a new invariant classification of spacetime. Buchert's kinematical backreaction is retained as a derived explanatory quantity rather than a separate axis, since it is already fixed by the expansion-variance and shear contributions. A single curvature normalisation is used for all Weyl diagnostics. The method is tested on six benchmarks, namely FLRW, Bianchi-I, Kasner, Lemaitre-Tolman-Bondi dust, scalar-perturbed FLRW, and tensor-perturbed FLRW. These benchmarks occupy distinct regions of the diagnostic space, and the magnetic Weyl contribution appears only in the tensor case. The classification remains stable under changes of perturbation amplitude, spatial resolution, averaging domain, constraint reliability, and a leading-order observer tilt. The curvature expressions for the exact benchmarks are verified symbolically against metric-derived Weyl invariants, and the supporting computer code, numerical results, tables, and figures are publicly available.

physics.gen-ph↗

arXiv2026

CapCLIP: A Vision-Language Representation Alignment Approach for Wireless Capsule Endoscopy Analysis

Wireless capsule endoscopy (WCE) enables non-invasive visual assessment of the small bowel, but its clinical utility is constrained by the large volume of frames generated per examination and the difficulty of recognising subtle abnormalities under highly variable imaging conditions. Existing learning-based approaches for WCE are predominantly vision-only, often confined to narrow pathology sets, and show limited transfer across datasets and centres. To address these limitations, this study introduces CapCLIP, a domain-specific vision-language representation learning framework for WCE. CapCLIP aligns capsule endoscopy frames with clinically grounded textual descriptions derived from standardised nomenclature and pathology-aware caption templates, thereby learning embeddings that are both semantically informed and transferable. The proposed framework is evaluated against relevant open-source vision and vision-language foundation models under strict zero-shot conditions using unseen WCE datasets. Evaluation covers three downstream tasks: K-nearest neighbour classification, CLIP-style image-text classification, and text-to-image retrieval. Across these settings, CapCLIP consistently outperforms the compared baselines, with particularly strong gains in zero-shot image-text classification and cross-modal retrieval on out-of-distribution datasets. The results indicate that language-guided representation learning can improve both generalisation and semantic interpretability in WCE analysis. These findings position CapCLIP as a step toward foundation models tailored to capsule endoscopy and support the use of language-grounded WCE analysis.

cs.CV↗

arXiv2026

Training Deep Visual Networks Beyond Loss and Accuracy Through a Dynamical Systems Approach

Deep visual recognition models are usually trained and evaluated using metrics such as loss and accuracy. While these measures show whether a model is improving, they reveal very little about how its internal representations change during training. This paper introduces a complementary way to study that process by examining training through the lens of dynamical systems. Drawing on ideas from signal analysis originally used to study biological neural activity, we define three measures from layer activations collected across training epochs: an integration score that reflects long-range coordination across layers, a metastability score that captures how flexibly the network shifts between more and less synchronised states, and a combined dynamical stability index. We apply this framework to nine combinations of model architecture and dataset, including several ResNet variants, DenseNet-121, MobileNetV2, VGG-16, and a pretrained Vision Transformer on CIFAR-10 and CIFAR-100. The results suggest three main patterns. First, the integration measure consistently distinguishes the easier CIFAR-10 setting from the more difficult CIFAR-100 setting. Second, changes in the volatility of the stability index may provide an early sign of convergence before accuracy fully plateaus. Third, the relationship between integration and metastability appears to reflect different styles of training behaviour. Overall, this study offers an exploratory but promising new way to understand deep visual training beyond loss and accuracy.

cs.CV↗

arXiv2026

Biharmonic Subdivision on Riemannian Manifolds

This paper introduces a biharmonic interpolatory subdivision framework on Riemannian manifolds. In the Euclidean setting, the six-point Deslauriers-Dubuc stencil is characterised as the unique minimiser of a discrete curvature-variation energy under symmetric six-point support and degree-five polynomial reproduction conditions, linking a classical interpolatory rule to a first-principles fairness criterion. Exact symbol analysis establishes fourth-order smoothness. The construction extends to the two-sphere and the hyperbolic plane via a second-order reduced governing ODE derived from the biharmonic Euler-Lagrange equation on constant-curvature surfaces. This reduced model yields closed-form insertion rules, and proximity analysis confirms that the manifold scheme satisfies the Wallner-Dyn second-order condition, preserving fourth-order smoothness. A hierarchy of biharmonic stencils achieving higher smoothness orders is also described. Numerical experiments demonstrate that the six-point scheme delivers lower fairness energy and smoother curvature profiles than the classical four-point Dyn-Gregory-Levin scheme, while remaining more local and exhibiting less ringing on non-uniform data than the eight-point variant.

math.GM↗

arXiv2026

A Neural Tension Operator for Curve Subdivision across Constant Curvature Geometries

Interpolatory subdivision schemes generate smooth curves from piecewise-linear control polygons by repeatedly inserting new vertices. Classical schemes rely on a single global tension parameter and typically require separate formulations in Euclidean, spherical, and hyperbolic geometries. We introduce a shared learned tension predictor that replaces the global parameter with per-edge insertion angles predicted by a single 140K-parameter network. The network takes local intrinsic features and a trainable geometry embedding as input, and the predicted angles drive geometry-specific insertion operators across all three spaces without architectural modification. A constrained sigmoid output head enforces a structural safety bound, guaranteeing that every inserted vertex lies within a valid angular range for any finite weight configuration. Three theoretical results accompany the method: a structural guarantee of tangent-safe insertions; a heuristic motivation for per-edge adaptivity; and a conditional convergence certificate for continuously differentiable limit curves, subject to an explicit Lipschitz constraint verified post hoc. On 240 held-out validation curves, the learned predictor occupies a distinct position on the fidelity--smoothness Pareto frontier, achieving markedly lower bending energy and angular roughness than all fixed-tension and manifold-lift baselines. Riemannian manifold lifts retain a pointwise-fidelity advantage, which this study quantifies directly. On the out-of-distribution ISS orbital ground-track example, bending energy falls by 41% and angular roughness by 68% with only a modest increase in Hausdorff distance, suggesting that the predictor generalises beyond its synthetic training distribution.

cs.LG↗

arXiv2026

Handcrafted Feature-Assisted One-Class Learning for Artist Authentication in Historical Drawings

Authentication and attribution of works on paper remain persistent challenges in cultural heritage, particularly when the available reference corpus is small and stylistic cues are primarily expressed through line and limited tonal variation. We present a verification-based computational framework for historical drawing authentication using one-class autoencoders trained on a compact set of interpretable handcrafted features. Ten artist-specific verifiers are trained using authenticated sketches from the Metropolitan Museum of Art open-access collection, the Ashmolean Collections Catalogue, the Morgan Library and Museum, the Royal Collection Trust (UK), the Victoria and Albert Museum Collections, and an online catalogue of the Casa Buonarroti collection and evaluated under a biometric-style protocol with genuine and impostor trials. Feature vectors comprise Fourier-domain energy, Shannon entropy, global contrast, GLCM-based homogeneity, and a box-counting estimate of fractal complexity. Across 900 verification decisions (90 genuine and 810 impostor trials), the pooled system achieves a True Acceptance Rate of 83.3% with a False Acceptance Rate of 9.5% at the chosen operating point. Performance varies substantially by artist, with near-zero false acceptance for some verifiers and elevated confusability for others. A pairwise attribution of false accepts indicates structured error pathways consistent with stylistic proximity and shared drawing conventions, whilst also motivating tighter control of digitisation artefacts and threshold calibration. The proposed methodology is designed to complement, rather than replace, connoisseurship by providing reproducible, quantitative evidence suitable for data-scarce settings common in historical sketch attribution.

cs.CV↗

arXiv2026

Dynamical Systems Analysis Reveals Functional Regimes in Large Language Models

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where temporal integration and metastability are core markers of neural organisation, we adapt these concepts to transformer models and discuss a composite dynamical metric, computed from activation time-series during autoregressive generation. We evaluate this metric in GPT-2-medium across five conditions: structured reasoning, forced repetition, high-temperature noisy sampling, attention-head pruning, and weight-noise injection. Structured reasoning consistently exhibits elevated metric relative to repetitive, noisy, and perturbed regimes, with statistically significant differences confirmed by one-way ANOVA and large effect sizes in key comparisons. These results are robust to layer selection, channel subsampling, and random seeds. Our findings demonstrate that neuroscience-inspired dynamical metrics can reliably characterise differences in computational organisation across functional regimes in large language models. We stress that the proposed metric captures formal dynamical properties and does not imply subjective experience.

cs.AI↗

arXiv2025

Quantifying the Dynamics of Consciousness using Hierarchical Integration, Organised Complexity and Metastability

Quantifying the neural signatures of consciousness remains a major challenge in neuroscience and AI. Although many theories link consciousness to rich, multiscale, and flexible neural organisation, robust quantitative measures are still lacking. This paper presents a theory-neutral framework that characterises consciousness-related dynamics through three properties: hierarchical integration (H), cross-frequency complexity (D), and metastability (M). Candidate subsystems are identified using predictive information, temporal complexity, and state-space exploration to distinguish structured from unstructured activity. We provide mathematical definitions for all components and implement the framework in a generative model of synthetic EEG, simulating nine brain states ranging from psychedelic and wakeful to dreaming, non-REM sleep, minimally conscious, anaesthetised, and seizure-like regimes. Across single trials and Monte Carlo ensembles, the composite index reliably separates high-consciousness from impaired or non-conscious states. We further validate the framework using real EEG from the Sleep-EDF dataset alongside matched synthetic EEG designed to reproduce state-dependent oscillatory structure. Across Wake, N2, and REM sleep, synthetic data recapitulate the empirical ordering and magnitude of the index, indicating that the index captures stable and biologically meaningful distinctions. This approach provides a principled and empirically grounded tool for quantifying consciousness-related neural organisation with potential applications to both biological and artificial systems.

q-bio.NC↗

arXiv2025

Integrating Visual and X-Ray Machine Learning Features in the Study of Paintings by Goya

Art authentication of Francisco Goya's works presents complex computational challenges due to his heterogeneous stylistic evolution and extensive historical patterns of forgery. We introduce a novel multimodal machine learning framework that applies identical feature extraction techniques to both visual and X-ray radiographic images of Goya paintings. The unified feature extraction pipeline incorporates Grey-Level Co-occurrence Matrix descriptors, Local Binary Patterns, entropy measures, energy calculations, and colour distribution analysis applied consistently across both imaging modalities. The extracted features from both visual and X-ray images are processed through an optimised One-Class Support Vector Machine with hyperparameter tuning. Using a dataset of 24 authenticated Goya paintings with corresponding X-ray images, split into an 80/20 train-test configuration with 10-fold cross-validation, the framework achieves 97.8% classification accuracy with a 0.022 false positive rate. Case study analysis of ``Un Gigante'' demonstrates the practical efficacy of our pipeline, achieving 92.3% authentication confidence through unified multimodal feature analysis. Our results indicate substantial performance improvement over single-modal approaches, establishing the effectiveness of applying identical computational methods to both visual and radiographic imagery in art authentication applications.

cs.CV↗

arXiv2025

Latent Diffusion Based Face Enhancement under Degraded Conditions for Forensic Face Recognition

Face recognition systems experience severe performance degradation when processing low-quality forensic evidence imagery. This paper presents an evaluation of latent diffusion-based enhancement for improving face recognition under forensically relevant degradations. Using a dataset of 3,000 individuals from LFW with 24,000 recognition attempts, we implement the Flux.1 Kontext Dev pipeline with Facezoom LoRA adaptation to test against seven degradation categories, including compression artefacts, blur effects, and noise contamination. Our approach demonstrates substantial improvements, increasing overall recognition accuracy from 29.1% to 84.5% (55.4 percentage point improvement, 95% CI: [54.1, 56.7]). Statistical analysis reveals significant performance gains across all degradation types, with effect sizes exceeding conventional thresholds for practical significance. These findings establish the potential of sophisticated diffusion based enhancement in forensic face recognition applications.

cs.CV↗

arXiv2025

A Lightweight Face Quality Assessment Framework to Improve Face Verification Performance in Real-Time Screening Applications

Face image quality plays a critical role in determining the accuracy and reliability of face verification systems, particularly in real-time screening applications such as surveillance, identity verification, and access control. Low-quality face images, often caused by factors such as motion blur, poor lighting conditions, occlusions, and extreme pose variations, significantly degrade the performance of face recognition models, leading to higher false rejection and false acceptance rates. In this work, we propose a lightweight yet effective framework for automatic face quality assessment, which aims to pre-filter low-quality face images before they are passed to the verification pipeline. Our approach utilises normalised facial landmarks in conjunction with a Random Forest Regression classifier to assess image quality, achieving an accuracy of 96.67%. By integrating this quality assessment module into the face verification process, we observe a substantial improvement in performance, including a comfortable 99.7% reduction in the false rejection rate and enhanced cosine similarity scores when paired with the ArcFace face verification model. To validate our approach, we have conducted experiments on a real-world dataset collected comprising over 600 subjects captured from CCTV footage in unconstrained environments within Dubai Police. Our results demonstrate that the proposed framework effectively mitigates the impact of poor-quality face images, outperforming existing face quality assessment techniques while maintaining computational efficiency. Moreover, the framework specifically addresses two critical challenges in real-time screening: variations in face resolution and pose deviations, both of which are prevalent in practical surveillance scenarios.

cs.CV↗