Hadi Zaatiti

Nina Miolane, Alice Le Brigant, Johan Mathe et al.

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at \url{geomstats.ai}.

Hadi Zaatiti, Hatem Hajri, Osama Abdullah et al.

Modern Arabic ASR systems such as wav2vec 2.0 excel at word- and sentence-level transcription, yet struggle to classify isolated letters. In this study, we show that this phoneme-level task, crucial for language learning, speech therapy, and phonetic research, is challenging because isolated letters lack co-articulatory cues, provide no lexical context, and last only a few hundred milliseconds. Recogniser systems must therefore rely solely on variable acoustic cues, a difficulty heightened by Arabic's emphatic (pharyngealized) consonants and other sounds with no close analogues in many languages. This study introduces a diverse, diacritised corpus of isolated Arabic letters and demonstrates that state-of-the-art wav2vec 2.0 models achieve only 35% accuracy on it. Training a lightweight neural network on wav2vec embeddings raises performance to 65%. However, adding a small amplitude perturbation (epsilon = 0.05) cuts accuracy to 32%. To restore robustness, we apply adversarial training, limiting the noisy-speech drop to 9% while preserving clean-speech accuracy. We detail the corpus, training pipeline, and evaluation protocol, and release, on demand, data and code for reproducibility. Finally, we outline future work extending these methods to word- and sentence-level frameworks, where precise letter pronunciation remains critical.

Thomas Gerald, Hadi Zaatiti, Hatem Hajri et al.

Detecting communities on graphs has received significant interest in recent literature. Current state-of-the-art community embedding approach called \textit{ComE} tackles this problem by coupling graph embedding with community detection. Considering the success of hyperbolic representations of graph-structured data in last years, an ongoing challenge is to set up a hyperbolic approach for the community detection problem. The present paper meets this challenge by introducing a Riemannian equivalent of \textit{ComE}. Our proposed approach combines hyperbolic embeddings with Riemannian K-means or Riemannian mixture models to perform community detection. We illustrate the usefulness of this framework through several experiments on real-world social networks and comparisons with \textit{ComE} and recent hyperbolic-based classification approaches.