In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are K clients whose individually chosen models are aggregated by a central server. The bounds depend on the compressibility of each client's algorithm while keeping other clients' algorithms un-compressed, and leveraging the fact that small changes in each local model change the aggregated model by a factor of only 1/K . Adopting a recently proposed approach by Sefidgaran et al., and extending it suitably to the distributed setting, enables smaller rate-distortion terms which are shown to translate into tighter generalization bounds. The bounds are then applied to the distributed support vector machines (SVM), suggesting that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of \mathcal{O}(\sqrt{\log(K)/K}) .

The signature kernel is a positive definite kernel for sequential and temporal data that has become increasingly popular in machine learning applications due to powerful theoretical guarantees, strong empirical performance, and recently introduced various scalable variations. In this chapter, we give a short introduction to $\texttt{KSig}$, a $\texttt{Scikit-Learn}$ compatible Python package that implements various GPU-accelerated algorithms for computing signature kernels, and performing downstream learning tasks. We also introduce a new algorithm based on tensor sketches which gives strong performance compared to existing algorithms. The package is available at https://github.com/tgcsaba/ksig.

This paper presents a new hybrid model for predicting German electricity prices. The algorithm is based on combining Gaussian Process Regression (GPR) and Support Vector Regression (SVR). While GPR is a competent model for learning the stochastic pattern within the data and interpolation, its performance for out-of-sample data is not very promising. By choosing a suitable data-dependent covariance function, we can enhance the performance of GPR for the tested German hourly power prices. However, since the out-of-sample prediction depends on the training data, the prediction is vulnerable to noise and outliers. To overcome this issue, a separate prediction is made using SVR, which applies margin-based optimization, having an advantage in dealing with non-linear processes and outliers, since only certain necessary points (support vectors) in the training data are responsible for regression. Both individual predictions are later combined using the performance-based weight assignment method. A test on historic German power prices shows that this approach outperforms its chosen benchmarks such as the autoregressive exogenous model, the naive approach, as well as the long short-term memory approach of prediction.

Quantum Machine Learning (QML) continues to evolve, unlocking new opportunities for diverse applications. In this study, we investigate and evaluate the applicability of QML models for binary classification of genome sequence data by employing various feature mapping techniques. We present an open-source, independent Qiskit-based implementation to conduct experiments on a benchmark genomic dataset. Our simulations reveal that the interplay between feature mapping techniques and QML algorithms significantly influences performance. Notably, the Pegasos Quantum Support Vector Classifier (Pegasos-QSVC) exhibits high sensitivity, particularly excelling in recall metrics, while Quantum Neural Networks (QNN) achieve the highest training accuracy across all feature maps. However, the pronounced variability in classifier performance, dependent on feature mapping, highlights the risk of overfitting to localized output distributions in certain scenarios. This work underscores the transformative potential of QML for genomic data classification while emphasizing the need for continued advancements to enhance the robustness and accuracy of these methodologies.

Supervised machine learning classifiers often encounter challenges related to performance, accuracy, and overfitting. This paper introduces the Artificial Liver Classifier (ALC), a novel supervised learning classifier inspired by the human liver's detoxification function. The ALC is characterized by its simplicity, speed, hyperparameters-free, ability to reduce overfitting, and effectiveness in addressing multi-classification problems through straightforward mathematical operations. To optimize the ALC's parameters, an improved FOX optimization algorithm (IFOX) is employed as the training method. The proposed ALC was evaluated on five benchmark machine learning datasets: Iris Flower, Breast Cancer Wisconsin, Wine, Voice Gender, and MNIST. The results demonstrated competitive performance, with the ALC achieving 100% accuracy on the Iris dataset, surpassing logistic regression, multilayer perceptron, and support vector machine. Similarly, on the Breast Cancer dataset, it achieved 99.12% accuracy, outperforming XGBoost and logistic regression. Across all datasets, the ALC consistently exhibited lower overfitting gaps and loss compared to conventional classifiers. These findings highlight the potential of leveraging biological process simulations to develop efficient machine learning models and open new avenues for innovation in the field.

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in settings where there is a shortage of training data or computational limitations exist. These methods are especially valued for their ability to work with small datasets and their interpretability. To address the issue of limited training data, mixup data augmentation, widely used in deep learning, has remained challenging to apply to learning in RKHS due to the generation of intermediate class labels. Although gradient descent methods handle these labels effectively, dual optimization approaches are typically not directly applicable. In this study, we present two novel algorithms that extend to a broader range of binary classification models. Unlike gradient-based approaches, our algorithms do not require hyperparameters like learning rates, simplifying their implementation and optimization. Both the number of iterations to converge and the computational cost per iteration scale linearly with respect to the dataset size. The numerical experiments demonstrate that our algorithms achieve faster convergence to the optimal solution compared to gradient descent approaches, and that mixup data augmentation consistently improves the predictive performance across various loss functions.

Large language model (LLM) architectures are often described as functionally hierarchical: Early layers process syntax, middle layers begin to parse semantics, and late layers integrate information. The present work revisits these ideas. This research submits simple texts to an LLM (e.g., "A church and organ") and extracts the resulting activations. Then, for each layer, support vector machines and ridge regressions are fit to predict a text's label and thus examine whether a given layer encodes some information. Analyses using a small model (Llama-3.2-3b; 28 layers) partly bolster the common hierarchical perspective: Item-level semantics are most strongly represented early (layers 2-7), then two-item relations (layers 8-12), and then four-item analogies (layers 10-15). Afterward, the representation of items and simple relations gradually decreases in deeper layers that focus on more global information. However, several findings run counter to a steady hierarchy view: First, although deep layers can represent document-wide abstractions, deep layers also compress information from early portions of the context window without meaningful abstraction. Second, when examining a larger model (Llama-3.3-70b-Instruct), stark fluctuations in abstraction level appear: As depth increases, two-item relations and four-item analogies initially increase in their representation, then markedly decrease, and afterward increase again momentarily. This peculiar pattern consistently emerges across several experiments. Third, another emergent effect of scaling is coordination between the attention mechanisms of adjacent layers. Across multiple experiments using the larger model, adjacent layers fluctuate between what information they each specialize in representing. In sum, an abstraction hierarchy often manifests across layers, but large models also deviate from this structure in curious ways.

We introduce a retrieval approach leveraging Support Vector Regression (SVR) ensembles, bootstrap aggregation (bagging), and embedding spaces on the German Dataset for Legal Information Retrieval (GerDaLIR). By conceptualizing the retrieval task in terms of multiple binary needle-in-a-haystack subtasks, we show improved recall over the baselines (0.849 > 0.803 | 0.829) using our voting ensemble, suggesting promising initial results, without training or fine-tuning any deep learning models. Our approach holds potential for further enhancement, particularly through refining the encoding models and optimizing hyperparameters.

As a natural evolution of traditional regression methods [3], ML models such as Support Vector Regression (SVR) [4] and Artificial Neural Networks (ANN) [5] have been developed to handle non-linear relationships and highdimensional datasets [6] with increasing accuracy and robustness. For instance, SVR has proven to be a robust regression tool because it can generalize well with limited data and capture nonlinear relationships using kernel functions [7]. Similarly, ANN, inspired by the neural architecture of the human brain, has become foundational to ML [5]. Typically, these methods use inputs (X) and outputs (Y) to construct surrogate models that aim to minimize the difference between the predicted and actual output values. These models have found applications across diverse fields, including engineering, medicine, and economics, demonstrating their versatility and potential [8], [9], [10]. In many real-world applications, additional prior information regarding the output model can be leveraged to enhance its accuracy and robustness [11] [12]. For instance, in physical systems, knowledge of the governing laws of physics has been successfully incorporated into ML by developing physics-informed neural networks (PINNs) [13], leading to improved efficiency and accuracy in prediction tasks [14]. In addition to physical laws, probabilistic information about the structure of the problem may also exist in practical scenarios [15]. Moreover, in many systems, the output variable is inherently probabilistic, necessitating models to approximate the probabilistic structure of the output [16].

The performance of pavement under loading depends on the strength of the subgrade. However, experimental estimation of properties of pavement strengths such as California bearing ratio (CBR), unconfined compressive strength (UCS) and resistance value (R) are often tedious, time-consuming and costly, thereby inspiring a growing interest in machine learning based tools which are simple, cheap and fast alternatives. Thus, the potential application of two boosting techniques; categorical boosting (CatBoost) and extreme gradient boosting (XGBoost) and support vector regression (SVR), is similarly explored in this study for estimation of properties of subgrade soil modified with hydrated lime activated rice husk ash (HARSH). Using 121 experimental data samples of varying proportions of HARSH, plastic limit, liquid limit, plasticity index, clay activity, optimum moisture content, and maximum dry density as input for CBR, UCS and R estimation, four evaluation metrics namely coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to evaluate the models' performance. The results indicate that XGBoost outperformed CatBoost and SVR in estimating these properties, yielding R2 of 0.9994, 0.9995 and 0.9999 in estimating the CBR, UCS and R respectively. Also, SVR outperformed CatBoost in estimating the CBR and R with R2 of 0.9997 respectively. On the other hand, CatBoost outperformed SVR in estimating the UCS with R2 of 0.9994. Feature sensitivity analysis shows that the three machine learning techniques are unanimous that increasing HARSH proportion lead to values of the estimated properties respectively. A comparison with previous results also shows superiority of XGBoost in estimating subgrade properties.