Federated Learning (FL) is a widespread and well-adopted paradigm of decentralised learning that allows training one model from multiple sources without the need to transfer data between participating clients directly. Since its inception in 2015, it has been divided into numerous subfields that deal with application-specific issues, such as data heterogeneity or resource allocation. One such sub-field, Clustered Federated Learning (CFL), deals with the problem of clustering the population of clients into separate cohorts to deliver personalised models. Although a few remarkable works have been published in this domain, the problem remains largely unexplored, as its basic assumptions and settings differ slightly from those of standard FL. In this work, we present One-Shot Clustered Federated Learning (OCFL), a clustering-agnostic algorithm that can automatically detect the earliest suitable moment for clustering. Our algorithm is based on computing the cosine distance between the gradients of the clients and a temperature measure that detects when the federated model starts to converge. We empirically evaluate our methodology by testing various one-shot clustering algorithms for over forty different tasks on five benchmark datasets. Our experiments showcase the good performance of our approach when used to perform CFL in an automated manner without the need to adjust hyperparameters. We also revisit the practical feasibility of CFL algorithms based on the gradients of the clients, providing firm evidence of the high efficiency of density-based clustering methods when used to differentiate between the loss surfaces of neural networks trained on different distributions. Moreover, by inspecting the feasibility of local explanations generated with the help of GradCAM, we can provide more insights into the relationship between personalisation and the explainability of local predictions.

Microbiomes not only underpin Earth's biogeochemical cycles but also play crucial roles in both engineered and natural ecosystems, such as the soil, wastewater treatment, and the human gut. However, microbiome engineering faces significant obstacles to surmount to deliver the desired improvements in microbiome control. Here, we use the backpropagation neural network (BPNN), optimized through differential evolution (DE-BP), to predict the microbial composition of activated sludge (AS) systems collected from wastewater treatment plants (WWTPs) located worldwide. Furthermore, we introduce a novel clustering algorithm termed Directional Position Nonlinear Emotional Preference Migration Behavior Clustering (DPNG-EPMC). This method is applied to conduct a clustering analysis of WWTPs across various feature attributes. Finally, we employ the Similar Time Generative Adversarial Networks (SiTime-GAN), to synthesize novel microbial compositions and feature attributes data. As a result, we demonstrate that the DE-BP model can provide superior predictions of the microbial composition. Additionally, we show that the DPNG-EPMC can be applied to the analysis of WWTPs under various feature attributes. Finally, we demonstrate that the SiTime-GAN model can generate valuable incremental synthetic data. Our results, obtained through predicting the microbial community and conducting analysis of WWTPs under various feature attributes, develop an understanding of the factors influencing AS communities.

Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is given by the exponential Gibbs-Boltzmann form, we introduce the framework of "hierarchical maximum entropy" to address these multilevel models. We demonstrate that Pareto optimal distributions, which maximize entropies across all levels of hierarchical transformations, can be obtained via renormalization-group procedures from theoretical physics. This is achieved by formulating multilevel extensions of the Gibbs variational principle and the Donsker-Varadhan variational representation of entropy. Moreover, we explore settings with hierarchical invariances that significantly simplify the renormalization-group procedures, enhancing computational efficiency: quadratic modular loss functions, logarithmic loss functions, and nearest-neighbor loss functions. This is accomplished through the introduction of the concept of parameter flows, which serves as an analog to renormalization flows in renormalization group theory. This work connects ideas from probability theory, information theory, and statistical mechanics.

Instance-dependent cost-sensitive (IDCS) classifiers offer a promising approach to improving cost-efficiency in credit scoring by tailoring loss functions to instance-specific costs. However, the impact of such loss functions on the stability of model explanations remains unexplored in literature, despite increasing regulatory demands for transparency. This study addresses this gap by evaluating the stability of Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP) when applied to IDCS models. Using four publicly available credit scoring datasets, we first assess the discriminatory power and cost-efficiency of IDCS classifiers, introducing a novel metric to enhance cross-dataset comparability. We then investigate the stability of SHAP and LIME feature importance rankings under varying degrees of class imbalance through controlled resampling. Our results reveal that while IDCS classifiers improve cost-efficiency, they produce significantly less stable explanations compared to traditional models, particularly as class imbalance increases, highlighting a critical trade-off between cost optimization and interpretability in credit scoring. Amid increasing regulatory scrutiny on explainability, this research underscores the pressing need to address stability issues in IDCS classifiers to ensure that their cost advantages are not undermined by unstable or untrustworthy explanations.

Recently, the benefit of heavily overparameterized models has been observed in machine learning tasks: models with enough capacity to easily cross the \emph{interpolation threshold} improve in generalization error compared to the classical bias-variance tradeoff regime. We demonstrate this behavior for the first time in particle physics data and explore when and where `double descent' appears and under which circumstances overparameterization results in a performance gain.

Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(θ)/g} dθ$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

Eye movements can reveal early signs of neurodegeneration, including those associated with Parkinson's Disease (PD). This work investigates the utility of a set of gaze-based features for the automatic screening of PD from different visual exploration tasks. For this purpose, a novel methodology is introduced, combining classic fixation/saccade oculomotor features (e.g., saccade count, fixation duration, scanned area) with features derived from gaze clusters (i.e., regions with a considerable accumulation of fixations). These features are automatically extracted from six exploration tests and evaluated using different machine learning classifiers. A Mixture of Experts ensemble is used to integrate outputs across tests and both eyes. Results show that ensemble models outperform individual classifiers, achieving an Area Under the Receiving Operating Characteristic Curve (AUC) of 0.95 on a held-out test set. The findings support visual exploration as a non-invasive tool for early automatic screening of PD.

Sample efficiency in the face of computationally expensive simulations is a common concern in surrogate modeling. Current strategies to minimize the number of samples needed are not as effective in simulated environments with wide state spaces. As a response to this challenge, we propose a novel method to efficiently sample simulated deterministic environments by using policies trained by Reinforcement Learning. We provide an extensive analysis of these surrogate-building strategies with respect to Latin-Hypercube sampling or Active Learning and Kriging, cross-validating performances with all sampled datasets. The analysis shows that a mixed dataset that includes samples acquired by random agents, expert agents, and agents trained to explore the regions of maximum entropy of the state transition distribution provides the best scores through all datasets, which is crucial for a meaningful state space representation. We conclude that the proposed method improves the state-of-the-art and clears the path to enable the application of surrogate-aided Reinforcement Learning policy optimization strategies on complex simulators.

Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving Loss (RPL), a loss function that preserves these properties by minimizing discrepancies between relationship matrices (e.g., Gram or cosine) of high-dimensional data and their low-dimensional embeddings. RPL trains neural networks for non-linear projections and is supported by error bounds derived from matrix perturbation theory. Initial experiments suggest that RPL reduces embedding dimensions while largely retaining performance on downstream tasks, likely due to its preservation of key vector space properties. While we describe here the use of RPL in dimensionality reduction, this loss can also be applied more broadly, for example to cross-domain alignment and transfer learning, knowledge distillation, fairness and invariance, dehubbing, graph and manifold learning, and federated learning, where distributed embeddings must remain geometrically consistent.

This paper presents a machine learning framework for the early detection of rug pull scams on decentralized exchanges (DEXs) within The Open Network (TON) blockchain. TON's unique architecture, characterized by asynchronous execution and a massive web2 user base from Telegram, presents a novel and critical environment for fraud analysis. We conduct a comprehensive study on the two largest TON DEXs, Ston.Fi and DeDust, fusing data from both platforms to train our models. A key contribution is the implementation and comparative analysis of two distinct rug pull definitions-TVL-based (a catastrophic liquidity withdrawal) and idle-based (a sudden cessation of all trading activity)-within a single, unified study. We demonstrate that Gradient Boosting models can effectively identify rug pulls within the first five minutes of trading, with the TVL-based method achieving superior AUC (up to 0.891) while the idle-based method excels at recall. Our analysis reveals that while feature sets are consistent across exchanges, their underlying distributions differ significantly, challenging straightforward data fusion and highlighting the need for robust, platform-aware models. This work provides a crucial early-warning mechanism for investors and enhances the security infrastructure of the rapidly growing TON DeFi ecosystem. Introduction The Open Network [1] was originally conceived and developed by Telegram, and is now independently operated by the TON Foundation. It is a high-performance decentralized platform designed to support large-scale decentralized applications (DApps) [2] and smart contracts [3].