This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we present a topological LMS algorithm that efficiently processes streaming signals observed over time-varying edge subsets. We provide a detailed stochastic analysis of the algorithm, deriving its stability conditions, steady-state mean-square-error, and convergence speed, while exploring the impact of edge sampling on performance. We also propose strategies to design optimal edge sampling probabilities, minimizing rate while ensuring desired estimation accuracy. Assuming partial knowledge of the complex structure (e.g., the underlying graph), we introduce an adaptive topology inference method that integrates with the proposed LMS framework. Additionally, we propose a distributed version of the algorithm and analyze its stability and mean-square-error properties. Empirical results on synthetic and real-world traffic data demonstrate that our approach, in both centralized and distributed settings, outperforms graph-based LMS methods by leveraging higher-order topological features.

This paper aims to develop an energy-efficient classifier for time-series data by introducing PatchEchoClassifier, a novel model that leverages a reservoir-based mechanism known as the Echo State Network (ESN). The model is designed for human activity recognition (HAR) using one-dimensional sensor signals and incorporates a tokenizer to extract patch-level representations. To train the model efficiently, we propose a knowledge distillation framework that transfers knowledge from a high-capacity MLP-Mixer teacher to the lightweight reservoir-based student model. Experimental evaluations on multiple HAR datasets demonstrate that our model achieves over 80 percent accuracy while significantly reducing computational cost. Notably, PatchEchoClassifier requires only about one-sixth of the floating point operations (FLOPS) compared to DeepConvLSTM, a widely used convolutional baseline. These results suggest that PatchEchoClassifier is a promising solution for real-time and energy-efficient human activity recognition in edge computing environments.

Machine Learning (ML) techniques for Optimal Power Flow (OPF) problems have recently garnered significant attention, reflecting a broader trend of leveraging ML to approximate and/or accelerate the resolution of complex optimization problems. These developments are necessitated by the increased volatility and scale in energy production for modern and future grids. However, progress in ML for OPF is hindered by the lack of standardized datasets and evaluation metrics, from generating and solving OPF instances, to training and benchmarking machine learning models. To address this challenge, this paper introduces PGLearn, a comprehensive suite of standardized datasets and evaluation tools for ML and OPF. PGLearn provides datasets that are representative of real-life operating conditions, by explicitly capturing both global and local variability in the data generation, and by, for the first time, including time series data for several large-scale systems. In addition, it supports multiple OPF formulations, including AC, DC, and second-order cone formulations. Standardized datasets are made publicly available to democratize access to this field, reduce the burden of data generation, and enable the fair comparison of various methodologies. PGLearn also includes a robust toolkit for training, evaluating, and benchmarking machine learning models for OPF, with the goal of standardizing performance evaluation across the field. By promoting open, standardized datasets and evaluation metrics, PGLearn aims at democratizing and accelerating research and innovation in machine learning applications for optimal power flow problems. Datasets are available for download at https://www.huggingface.co/PGLearn.

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.

Foundation models serve as the backbone for numerous specialized models developed through fine-tuning. However, when the underlying pretrained model is updated or retrained (e.g., on larger and more curated datasets), the fine-tuned model becomes obsolete, losing its utility and requiring retraining. This raises the question: is it possible to transfer fine-tuning to a new release of the model? In this work, we investigate how to transfer fine-tuning to a new checkpoint without having to re-train, in a data-free manner. To do so, we draw principles from model re-basin and provide a recipe based on weight permutations to re-base the modifications made to the original base model, often called task vector. In particular, our approach tailors model re-basin for Transformer models, taking into account the challenges of residual connections and multi-head attention layers. Specifically, we propose a two-level method rooted in spectral theory, initially permuting the attention heads and subsequently adjusting parameters within select pairs of heads. Through extensive experiments on visual and textual tasks, we achieve the seamless transfer of fine-tuned knowledge to new pre-trained backbones without relying on a single training step or datapoint. Code is available at https://github.com/aimagelab/TransFusion.

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.

Detecting vehicles in satellite images is crucial for traffic management, urban planning, and disaster response. However, current models struggle with real-world diversity, particularly across different regions. This challenge is amplified by geographic bias in existing datasets, which often focus on specific areas and overlook regions like the Middle East. To address this gap, we present the Vehicles in the Middle East (VME) dataset, designed explicitly for vehicle detection in high-resolution satellite images from Middle Eastern countries. Sourced from Maxar, the VME dataset spans 54 cities across 12 countries, comprising over 4,000 image tiles and more than 100,000 vehicles, annotated using both manual and semi-automated methods. Additionally, we introduce the largest benchmark dataset for Car Detection in Satellite Imagery (CDSI), combining images from multiple sources to enhance global car detection. Our experiments demonstrate that models trained on existing datasets perform poorly on Middle Eastern images, while the VME dataset significantly improves detection accuracy in this region. Moreover, state-of-the-art models trained on CDSI achieve substantial improvements in global car detection.

Remote sensing (RS) imagery, which requires specialized satellites to collect and is difficult to annotate, suffers from data scarcity and class imbalance in certain spectrums. Due to their data scarcity, training large-scale RS models from scratch is unrealistic, and the alternative is to transfer pre-trained models by fine-tuning or a more data-efficient method LoRA. Due to class imbalance, transferred models exhibit strong bias, where features of the major class dominate over those of the minor class. In this paper, we propose debLoRA, a generic training approach that works with any LoRA variants to yield debiased features. It is an unsupervised learning approach that can diversify minor class features based on the shared attributes with major classes, where the attributes are obtained by a simple step of clustering.

In this paper, a Bayesian nonparametric (BNP) model for Baxter permutations (BPs), termed BP process (BPP) is proposed and applied to relational data analysis. The BPs are a well-studied class of permutations, and it has been demonstrated that there is one-to-one correspondence between BPs and several interesting objects including floorplan partitioning (FP), which constitutes a subset of rectangular partitioning (RP). Accordingly, the BPP can be used as an FP model. We combine the BPP with a multi-dimensional extension of the stick-breaking process called the block-breaking process to fill the gap between FP and RP, and obtain a stochastic process on arbitrary RPs. Compared with conventional BNP models for arbitrary RPs, the proposed model is simpler and has a high affinity with Bayesian inference.

Imagine: China deploys hundreds of thousands of autonomous drones in the air, on the sea, and under the water--all armed with explosive warheads or small missiles. These machines descend in a swarm toward military installations on Taiwan and nearby US bases, and over the course of a few hours, a single robotic blitzkrieg overwhelms the US Pacific force before it can even begin to fight back. The proliferation of cheap drones means just about any group with the wherewithal to assemble and launch a swarm could wreak havoc, no expensive jets or massive missile installations required. The US armed forces are now hunting for a solution--and they want it fast. Every branch of the service and a host of defense tech startups are testing out new weapons that promise to disable drones en masse.