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Hiba Nassar

Publications and source records attributed to Hiba Nassar.

14 recordsLinked to original sources
arXiv2026

On the modality gap and the contrastive loss in multi-modal representation learning

We study the modality gap in CLIP-style dual-encoder contrastive learning, where image and text embeddings remain misaligned despite being trained in a shared space. We argue that the gap is induced by a failure of the InfoNCE formulation with independent encoders. We conduct a uni-modal experiment with two independent encoders and identical initialization conditions and find that InfoNCE actively generates a gap at low temperatures. We provide a theoretical analysis of this phenomenon and show that the modality gap is indeed a mode-failure of InfoNCE, but only at low temperatures. We propose a simple modification called xNCE, which uses intermodal as well as intra-modality negative contrastive pairs. xNCE matches retrieval performance on MS-COCO while consistently reducing the gap even at low temperatures. Notably, xNCE improves zero-shot classification over the InfoNCE baseline across all benchmarks, whereas high-temperature InfoNCE and regularized InfoNCE both fail to do so, demonstrating that xNCE reduces the modality gap without sacrificing the discriminative geometry needed for transfer.

cs.LG↗
arXiv2026

Improving Relative Representations with Learned Anchors and Whitened Inner Products

Independently trained neural models typically converge to incompatible latent representations, creating a fundamental barrier to highly modular AI systems. While Relative Representations (RR) address this by mapping absolute coordinates to a shared space defined by similarities to common anchor points, traditional implementations rely on randomly sampled anchors and cosine similarity, which frequently fail to capture the anisotropic geometries of modern architectures like Transformers. In this work, we propose a robust framework for cross-model communication based on two improvements. We learn anchors as robust semantic prototypes and utilize a geometry-aware similarity metric which preserves discriminative magnitude information and is invariant to affine shifts. Our approach demonstrates significant gains in performance and consistency across vision and language tasks. Notably, it enables nearly lossless information transfer and stable zero-shot communication even between highly heterogeneous architectures, such as small language models of varying scales.

cs.LG↗
arXiv2026

On What We Can Learn from Low-Resolution Data

Artificial intelligence systems typically rely on large, centrally collected datasets, a premise that does not hold in many real-world domains such as healthcare and public institutions. In these settings, data sharing is often constrained by storage, privacy, or resource limitations. For example, small wearable devices may lack the bandwidth or energy capacity needed to store and transmit high-resolution data, leading to aggregation during data collection and thus a loss of information. As a result, datasets collected from different sources may consist of a mixture of high- and low-resolution samples. Despite the prevalence of this setting, it remains unclear how informative low-resolution data is when models are ultimately evaluated on high-resolution inputs. We provide a theoretical analysis based on the Kullback-Leibler divergence that characterises how the influence of a datapoint changes with resolution, and derive bounds that relate the relative contribution of high- and low-resolution observations to the information lost under downsampling. To support this analysis, we empirically demonstrate, using both a vision transformer and a convolutional neural network, that adding low-resolution data to the training set consistently improves performance when high-resolution data is scarce.

cs.LG↗
arXiv2024

Spline Based Methods for Functional Data on Multivariate Domains

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a significant impact on the second phase of the analysis, as shown in recent research, where data-driven spline bases outperformed the predefined rigid choice of functional representation. The method chooses an initial functional basis by an efficient placement of the knots using a simple machine-learning algorithm. The approach does not apply directly when the data are defined on domains of a higher dimension than one such as, for example, images. The reason is that in higher dimensions the convenient and numerically efficient spline bases are obtained as tensor bases from 1D spline bases that require knots that are located on a lattice. This does not allow for a flexible knot placement that was fundamental for the 1D approach. The goal of this research is to propose two modified approaches that circumvent the problem by coding the irregular knot selection into their densities and utilizing these densities through the topology of the spaces of splines. This allows for regular grids for the knots and thus facilitates using the spline tensor bases. It is tested on 1D data showing that its performance is comparable to or better than the previous methods.

stat.AP↗
arXiv2024

Efficient spline orthogonal basis for representation of density functions

Probability density functions form a specific class of functional data objects with intrinsic properties of scale invariance and relative scale characterized by the unit integral constraint. The Bayes spaces methodology respects their specific nature, and the centred log-ratio transformation enables processing such functional data in the standard Lebesgue space of square-integrable functions. As the data representing densities are frequently observed in their discrete form, the focus has been on their spline representation. Therefore, the crucial step in the approximation is to construct a proper spline basis reflecting their specific properties. Since the centred log-ratio transformation forms a subspace of functions with a zero integral constraint, the standard $B$-spline basis is no longer suitable. Recently, a new spline basis incorporating this zero integral property, called $Z\!B$-splines, was developed. However, this basis does not possess the orthogonal property which is beneficial from computational and application point of view. As a result of this paper, we describe an efficient method for constructing an orthogonal $Z\!B$-splines basis, called $Z\!B$-splinets. The advantages of the $Z\!B$-splinet approach are foremost a computational efficiency and locality of basis supports that is desirable for data interpretability, e.g. in the context of functional principal component analysis. The proposed approach is demonstrated on an empirical demographic dataset.

stat.ME↗
arXiv2023

Splinets -- Orthogonal Splines and FDA for the Classification Problem

This study introduces an efficient workflow for functional data analysis in classification problems, utilizing advanced orthogonal spline bases. The methodology is based on the flexible Splinets package, featuring a novel spline representation designed for enhanced data efficiency. Several innovative features contribute to this efficiency: 1)Utilization of Orthonormal Spline Bases 2)Consideration of Spline Support Sets 3)Data-Driven Knot Selection. Illustrating this approach, we applied the workflow to the Fashion MINST dataset. We demonstrate the classification process and highlight significant efficiency gains. Particularly noteworthy are the improvements that can be achieved through the 2D generalization of our methodology, especially in scenarios where data sparsity and dimension reduction are critical factors. A key advantage of our workflow is the projection operation into the space of splines with arbitrarily chosen knots, allowing for versatile functional data analysis associated with classification problems. Moreover, the study explores Splinets package features suited for functional data analysis. The algebra and calculus of splines use Taylor expansions at the knots within the support sets. Various orthonormalization techniques for B-splines are implemented, including the highly recommended dyadic method, which leads to the creation of splinets. Importantly, the locality of B-splines concerning support sets is preserved in the corresponding splinet. Using this locality, along with implemented algorithms, provides a powerful computational tool for functional data analysis.

stat.ME↗
arXiv2023

Splinets 1.5.0 -- Periodic Splinets

Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects representing such splines and describes how an efficient orthogonal basis can be obtained. The proposed orthonormalized basis is called a periodic splinet in the reference to earlier work where analogous concepts and tools have been introduced for splines on an interval. Based on this methodology, the periodic splines and splinets are added to the earlier version of the R package "Splinets". Moreover, the developed computational tools have been applied to functionally analyze a standard example of functional circular data of wind directions and speeds.

math.NA↗
arXiv2022

Analysing the Influence of Attack Configurations on the Reconstruction of Medical Images in Federated Learning

The idea of federated learning is to train deep neural network models collaboratively and share them with multiple participants without exposing their private training data to each other. This is highly attractive in the medical domain due to patients' privacy records. However, a recently proposed method called Deep Leakage from Gradients enables attackers to reconstruct data from shared gradients. This study shows how easy it is to reconstruct images for different data initialization schemes and distance measures. We show how data and model architecture influence the optimal choice of initialization scheme and distance measure configurations when working with single images. We demonstrate that the choice of initialization scheme and distance measure can significantly increase convergence speed and quality. Furthermore, we find that the optimal attack configuration depends largely on the nature of the target image distribution and the complexity of the model architecture.

eess.IV↗
arXiv2021

Minimal Model Structure Analysis for Input Reconstruction in Federated Learning

\ac{fl} proposed a distributed \ac{ml} framework where every distributed worker owns a complete copy of global model and their own data. The training is occurred locally, which assures no direct transmission of training data. However, the recent work \citep{zhu2019deep} demonstrated that input data from a neural network may be reconstructed only using knowledge of gradients of that network, which completely breached the promise of \ac{fl} and sabotaged the user privacy. In this work, we aim to further explore the theoretical limits of reconstruction, speedup and stabilize the reconstruction procedure. We show that a single input may be reconstructed with the analytical form, regardless of network depth using a fully-connected neural network with one hidden node. Then we generalize this result to a gradient averaged over batches of size $B$. In this case, the full batch can be reconstructed if the number of hidden units exceeds $B$. For a \ac{cnn}, the number of required kernels in convolutional layers is decided by multiple factors, e.g., padding, kernel and stride size, etc. We require the number of kernels $h\geq (\frac{d}{d^{\prime}})^2C$, where we define $d$ as input width, $d^{\prime}$ as output width after convolutional layer, and $C$ as channel number of input. We validate our observation and demonstrate the improvements using bio-medical (fMRI, \ac{wbc}) and benchmark data (MNIST, Kuzushiji-MNIST, CIFAR100, ImageNet and face images).

cs.CR↗
arXiv2021

Machine Learning Assisted Orthonormal Basis Selection for Functional Data Analysis

In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered to transform observed functional data and a choice is made without any formal criteria indicating which of the bases is preferable for the initial transformation of the data into functions. In an attempt to address this issue, we propose a strictly data-driven method of orthogonal basis selection. The method uses recently introduced orthogonal spline bases called the splinets obtained by efficient orthogonalization of the B-splines. The algorithm learns from the data in the machine learning style to efficiently place knots. The optimality criterion is based on the average (per functional data point) mean square error and is utilized both in the learning algorithms and in comparison studies. The latter indicates efficiency that is particularly evident for the sparse functional data and to a lesser degree in analyses of responses to complex physical systems.

stat.ML↗
arXiv2020

Splinets -- efficient orthonormalization of the B-splines

A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them. For this reason, the basis is referred to as a splinet. The splinets feature clear advantages over other spline bases. They efficiently exploit 'near-orthogonalization' featured by the B-splines and gains are achieved at two levels: locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to achieve orthogonality. These efficiencies are formally proven by showing the asymptotic rates with respect to the number of elements in a splinet. The natural symmetry of the B-splines in the case of the equally spaced knots is preserved in the splinets, while quasi-symmetrical features are also seen for the case of arbitrarily spaced knots.

math.ST↗
arXiv2013

A Functional Hodrick Prescott Filter

We propose a functional version of the Hodrick-Prescott filter for functional data which take values in an infinite dimensional separable Hilbert space. We further characterize the associated optimal smoothing parameter when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

math.ST↗
arXiv2013

On the functional Hodrick-Prescott Filter with non-compact operators

We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associated optimal smoothing operator preserves the structure obtained in the compact case, when the underlying distribution of the data is Gaussian.

math.ST↗