arXiv subjects

Verlon Roel Mbingui

Publications and source records attributed to Verlon Roel Mbingui.

6 recordsLinked to original sources

arXiv2026

Optimal Stochastic Krylov based Techniques for Large- Scale Log-Determinant Estimation

Estimating the logarithm of the determinant of large sparse positive definite symmetric matrices is an important task in numerical linear algebra, machine learning, Gaussian processes, and uncertainty quantification. In this work, we introduce two scalable and efficient methods for large-scale log-determinant termed the Optimal Stochastic Arnoldi with Incomplete Orthogonalization Procedure (OSA-IOP) and the Optimal Stochastic Lanczos Quadrature (OSLQ). The OSA-IOP approach extends the Incomplete Orthogonalization Procedure (IOP), originally developed for matrix exponential functions for exponential time stepping integrators, to compute the action of the matrix algorithm on a vector. We observe that combining IOP with a randomized Hutch++ algorithm, the OSA-IOP significantly reduces computational cost while maintaining high accuracy. The OSLQ method estimates log-determinants by coupling Lanczos quadrature with Hutch++ and controlled orthogonalization, leveraging Krylov subspaces as efficient quadrature mechanisms to approximate quadratic forms involving the matrix logarithm. We derive error bounds for both methods. Extensive numerical experiments on large-scale sparse matrices from real-world applications demonstrate the accuracy, robustness, and scalability of the proposed approaches.

math.NA↗

arXiv2026

Vision Tiny Recursion Model (ViTRM): Parameter-Efficient Image Classification via Recursive State Refinement

The success of deep learning in computer vision has been driven by models of increasing scale, from deep Convolutional Neural Networks (CNN) to large Vision Transformers (ViT). While effective, these architectures are parameter-intensive and demand significant computational resources, limiting deployment in resource-constrained environments. Inspired by Tiny Recursive Models (TRM), which show that small recursive networks can solve complex reasoning tasks through iterative state refinement, we introduce the \textbf{Vision Tiny Recursion Model (ViTRM)}: a parameter-efficient architecture that replaces the $L$-layer ViT encoder with a single tiny $k$-layer block ($k{=}3$) applied recursively $N$ times. Despite using up to $6 \times $ and $84 \times$ fewer parameters than CNN based models and ViT respectively, ViTRM maintains competitive performance on CIFAR-10 and CIFAR-100. This demonstrates that recursive computation is a viable, parameter-efficient alternative to architectural depth in vision.

cs.CV↗

arXiv2026

Splines-Based Feature Importance in Kolmogorov-Arnold Networks: A Framework for Supervised Tabular Data Dimensionality Reduction

Feature selection is a key step in many tabular prediction problems, where multiple candidate variables may be redundant, noisy, or weakly informative. We investigate feature selection based on Kolmogorov-Arnold Networks (KANs), which parameterize feature transformations with splines and expose per-feature importance scores in a natural way. From this idea we derive four KAN-based selection criteria (coefficient norms, gradient-based saliency, and knockout scores) and compare them with standard methods such as LASSO, Random Forest feature importance, Mutual Information, and SVM-RFE on a suite of real and synthetic classification and regression datasets. Using average F1 and $R^2$ scores across three feature-retention levels (20%, 40%, 60%), we find that KAN-based selectors are generally competitive with, and sometimes superior to, classical baselines. In classification, KAN criteria often match or exceed existing methods on multi-class tasks by removing redundant features and capturing nonlinear interactions. In regression, KAN-based scores provide robust performance on noisy and heterogeneous datasets, closely tracking strong ensemble predictors; we also observe characteristic failure modes, such as overly aggressive pruning with an $\ell_1$ criterion. Stability and redundancy analyses further show that KAN-based selectors yield reproducible feature subsets across folds while avoiding unnecessary correlation inflation, ensuring reliable and non-redundant variable selection. Overall, our findings demonstrate that KAN-based feature selection provides a powerful and interpretable alternative to traditional methods, capable of uncovering nonlinear and multivariate feature relevance beyond sparsity or impurity-based measures.

cs.LG↗

arXiv2026

Novel technique based on Léja Points Approximation for Log-determinant Estimation of Large matrices

The computation of the Log-determinant of large, sparse, symmetric positive definite (SPD) matrices is essential in many scientific computational fields such as numerical linear algebra and machine learning. In low dimensions, Cholesky is preferred, but in high dimensions, its computation may be prohibitive due to memory limitation. To circumvent this, Krylov subspace techniques have proven to be efficient but may be computationally expensive due to the required orthogonalization processes. In this paper, we introduce a novel technique to estimate the Log-determinant of a matrix using Léja points, where the implementation is only based on matrix multiplications and a rough estimation of eigenvalue bounds of the matrix. By coupling Léja points interpolation with a randomized algorithm called Hutch++, we achieve substantial reductions in computational complexity while preserving significant accuracy compared to the stochastic Lanczos quadrature. We establish the approximation errors of the matrix function together with multiplicative error bounds for the approximations obtained by this method. The effectiveness and scalability of the proposed method on both large sparse synthetic matrices (maximum likelihood in Gaussian Markov Random fields) and large-scale real-world matrices are confirmed through numerical experiments.

math.NA↗

arXiv2025

A comparative study of Bitcoin and Ripple cryptocurrencies trading using Deep Reinforcement Learning algorithms

Artificial intelligence (AI) has demonstrated remarkable success across various applications. In light of this trend, the field of automated trading has developed a keen interest in leveraging AI techniques to forecast the future prices of financial assets. This interest stems from the need to address trading challenges posed by the inherent volatility and dynamic nature of asset prices. However, crafting a flawless strategy becomes a formidable task when dealing with assets characterized by intricate and ever-changing price dynamics. To surmount these formidable challenges, this research employs an innovative rule-based strategy approach to train Deep Reinforcement Learning (DRL). This application is carried out specifically in the context of trading Bitcoin (BTC) and Ripple (XRP). Our proposed approach hinges on the integration of Deep Q-Network, Double Deep Q-Network, Dueling Deep Q-learning networks, alongside the Advantage Actor-Critic algorithms. Each of them aims to yield an optimal policy for our application. To evaluate the effectiveness of our Deep Reinforcement Learning (DRL) approach, we rely on portfolio wealth and the trade signal as performance metrics. The experimental outcomes highlight that Duelling and Double Deep Q-Network outperformed when using XRP with the increasing of the portfolio wealth. All codes are available in this \href{https://github.com/VerlonRoelMBINGUI/RL_Final_Projects_AMMI2023}{\color{blue}Github link}.

cs.CE↗

arXiv2025

Localized Weather Prediction Using Kolmogorov-Arnold Network-Based Models and Deep RNNs

Weather forecasting is crucial for managing risks and economic planning, particularly in tropical Africa, where extreme events severely impact livelihoods. Yet, existing forecasting methods often struggle with the region's complex, non-linear weather patterns. This study benchmarks deep recurrent neural networks such as $\texttt{LSTM, GRU, BiLSTM, BiGRU}$, and Kolmogorov-Arnold-based models $(\texttt{KAN} and \texttt{TKAN})$ for daily forecasting of temperature, precipitation, and pressure in two tropical cities: Abidjan, Cote d'Ivoire (Ivory Coast) and Kigali (Rwanda). We further introduce two customized variants of $ \texttt{TKAN}$ that replace its original $\texttt{SiLU}$ activation function with $ \texttt{GeLU}$ and \texttt{MiSH}, respectively. Using station-level meteorological data spanning from 2010 to 2024, we evaluate all the models on standard regression metrics. $\texttt{KAN}$ achieves temperature prediction ($R^2=0.9986$ in Abidjan, $0.9998$ in Kigali, $\texttt{MSE} < 0.0014~^\circ C ^2$), while $\texttt{TKAN}$ variants minimize absolute errors for precipitation forecasting in low-rainfall regimes. The customized $\texttt{TKAN}$ models demonstrate improvements over the standard $\texttt{TKAN}$ across both datasets. Classical \texttt{RNNs} remain highly competitive for atmospheric pressure ($R^2 \approx 0.83{-}0.86$), outperforming $\texttt{KAN}$-based models in this task. These results highlight the potential of spline-based neural architectures for efficient and data-efficient forecasting.

cs.LG↗