Salman Ahmadi-Asl

Ashish Jha, Dimitrii Ermilov, Konstantin Sobolev et al.

Pedestrian Attribute Recognition (PAR) focuses on identifying various attributes in pedestrian images, with key applications in person retrieval, suspect re-identification, and soft biometrics. However, Deep Neural Networks (DNNs) for PAR often suffer from over-parameterization and high computational complexity, making them unsuitable for resource-constrained devices. Traditional tensor-based compression methods typically factorize layers without adequately preserving the gradient direction during compression, leading to inefficient compression and a significant accuracy loss. In this work, we propose a novel approach for determining the optimal ranks of low-rank layers, ensuring that the gradient direction of the compressed model closely aligns with that of the original model. This means that the compressed model effectively preserves the update direction of the full model, enabling more efficient compression for PAR tasks. The proposed procedure optimizes the compression ranks for each layer within the ALM model, followed by compression using CPD-EPC or truncated SVD. This results in a reduction in model complexity while maintaining high performance.

Valentin Leplat, Salman Ahmadi-Asl, Junjun Pan et al.

Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time series). Yet practical and numerically reliable software support remains far less mature than those based on the real/complex setting. Here, we present QuatIca, an open-source Python library for quaternion numerical linear algebra and optimization, designed for both research prototyping and reproducible experimentation. QuatIca provides core quaternion matrix operations and norms; dense decompositions and reductions (QR, LU, Q-SVD, eigendecomposition, Hessenberg/tridiagonal reduction, Cholesky decomposition, and Schur helpers); iterative solvers including quaternion GMRES (with preconditioning) and Newton-Schulz pseudoinverse schemes; and domain-focused routines for signal and image processing such as quaternion Tikhonov restoration. The library also includes OptiQ, which solves quaternion Hermitian semidefinite programs using log-det barrier Newton methods with $μ$-continuation. We highlight design choices that preserve quaternion structure, and we provide end-to-end demonstrations including quaternion image deblurring, Lorenz-attractor filtering, and quaternion image completion. QuatIca is distributed via PyPI and accompanied by open-source development on GitHub and continuously deployed documentation with runnable tutorials.

Salman Ahmadi-Asl, Valentin Leplat, Anh-Huy Phan et al.

We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an order-$(N+1)$ tensor with a distinguished tube mode, the proposed representation consists of two third-order boundary cores and $N-2$ fourth-order interior cores linked through the t-product. As a result, for bounded tubal ranks, the storage scales linearly with the number of modes, in contrast to direct high-order extensions of T-SVD. We present two computational strategies: a sequential fixed-rank construction, called TTT-SVD, and a Fourier-slice alternating scheme based on the alternating two-cores update (ATCU). We also state a TT-SVD-type error bound for TTT-SVD and illustrate the practical performance of the proposed model on image compression, video compression, tensor completion, and hyperspectral imaging.

Salman Ahmadi-Asl, Malihe Nobakht Kooshkghazi, Valentin Leplat

Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input matrix-which is critical in modern computing environments dominated by communication costs. We address this gap by proposing a suite of pass-efficient randomized algorithms that let users directly trade pass budget for approximation accuracy. Our contributions include: (i) a family of arbitrary-pass randomized algorithms for low-rank approximation of quaternion matrices that operate under a user-specified number of matrix views, and (ii) a pass-efficient extension of block Krylov subspace methods that accelerates convergence for matrices with slowly decaying spectra. Furthermore, we establish spectral norm error bounds showing that the expected approximation error decays exponentially with the number of passes. Finally, we validate our framework through extensive numerical experiments and demonstrate its practical relevance across multiple applications, including quaternionic data compression, matrix completion, image super-resolution, and deep learning.

Malihe Nobakht Kooshkghazi, Salman Ahmadi-Asl, Andre L. F. de Almeida

This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental experiments using synthetics and real-world data are conducted to verify the efficiency and feasibility of the proposed randomized approach, and the numerical results show that the proposed method provides promising results. Applications of the proposed approach to data completion and data compression are presented.

Ashish Jha, Salman Ahmadi-Asl

Training modern neural networks on large datasets is computationally and energy intensive. We present SAGE, a streaming data-subset selection method that maintains a compact Frequent Directions (FD) sketch of gradient geometry in $O(\ell D)$ memory and prioritizes examples whose sketched gradients align with a consensus direction. The approach eliminates $N \times N$ pairwise similarities and explicit $N \times \ell$ gradient stores, yielding a simple two-pass, GPU-friendly pipeline. Leveraging FD's deterministic approximation guarantees, we analyze how agreement scoring preserves gradient energy within the principal sketched subspace. Across multiple benchmarks, SAGE trains with small kept-rate budgets while retaining competitive accuracy relative to full-data training and recent subset-selection baselines, and reduces end-to-end compute and peak memory. Overall, SAGE offers a practical, constant-memory alternative that complements pruning and model compression for efficient training.

Maame G. Asante-Mensah, Anh Huy Phan, Salman Ahmadi-Asl et al.

This paper presents a pixel selection method for compact image representation based on superpixel segmentation and tensor completion. Our method divides the image into several regions that capture important textures or semantics and selects a representative pixel from each region to store. We experiment with different criteria for choosing the representative pixel and find that the centroid pixel performs the best. We also propose two smooth tensor completion algorithms that can effectively reconstruct different types of images from the selected pixels. Our experiments show that our superpixel-based method achieves better results than uniform sampling for various missing ratios.