Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts. The Gumbel-Sinkhorn method, while effective, requires N*N parameters to determine a full permutation matrix, making it computationally expensive for large datasets. Low-rank matrix factorization approximations reduce memory requirements to 2MN (with M << N), but they still struggle with very large problems. SoftSort, by providing a continuous relaxation of the argsort operator, allows differentiable 1D sorting, but it faces challenges with multidimensional data and complex permutations. In this paper, we present a novel method for learning permutations using only N parameters, which dramatically reduces storage costs. Our approach builds on SoftSort, but extends it by iteratively shuffling the N indices of the elements to be sorted through a separable learning process. This modification significantly improves sorting quality, especially for multidimensional data and complex optimization criteria, and outperforms pure SoftSort. Our method offers improved memory efficiency and scalability compared to existing approaches, while maintaining high-quality permutation learning. Its dramatically reduced memory requirements make it particularly well-suited for large-scale optimization tasks, such as "Self-Organizing Gaussians", where efficient and scalable permutation learning is critical.

This paper introduces the Heteroscedastic AddiVortes model, a Bayesian non-parametric regression framework that simultaneously models the conditional mean and variance of a response variable using adaptive Voronoi tessellations. By employing a sum-of-tessellations approach for the mean and a product-of-tessellations approach for the variance, the model provides a flexible and interpretable means to capture complex, predictor-dependent relationships and heteroscedastic patterns in data. This dual-layer representation enables precise inference, even in high-dimensional settings, while maintaining computational feasibility through efficient Markov Chain Monte Carlo (MCMC) sampling and conjugate prior structures. We illustrate the model's capability through both simulated and real-world datasets, demonstrating its ability to capture nuanced variance structures, provide reliable predictive uncertainty quantification, and highlight key predictors influencing both the mean response and its variability. Empirical results show that the Heteroscedastic AddiVortes model offers a substantial improvement in capturing distributional properties compared to both homoscedastic and heteroscedastic alternatives, making it a robust tool for complex regression problems in various applied settings.

Large Language Models (LLMs) have revolutionized various Natural Language Generation (NLG) tasks, including Argument Summarization (ArgSum), a key subfield of Argument Mining (AM). This paper investigates the integration of state-of-the-art LLMs into ArgSum, including for its evaluation. In particular, we propose a novel prompt-based evaluation scheme, and validate it through a novel human benchmark dataset. Our work makes three main contributions: (i) the integration of LLMs into existing ArgSum frameworks, (ii) the development of a new LLM-based ArgSum system, benchmarked against prior methods, and (iii) the introduction of an advanced LLM-based evaluation scheme. We demonstrate that the use of LLMs substantially improves both the generation and evaluation of argument summaries, achieving state-of-the-art results and advancing the field of ArgSum.

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this study, we propose a novel functional output regression model based on kernel methods. Unlike conventional approaches that independently train regressors with scalar outputs for each measurement point of the output function, our method leverages the covariance structure within the function values, akin to multitask learning, leading to enhanced learning efficiency and improved prediction accuracy. Compared with existing nonlinear function-on-scalar models in statistical functional data analysis, our model effectively handles high-dimensional nonlinearity while maintaining a simple model structure. Furthermore, the fully kernel-based formulation allows the model to be expressed within the framework of reproducing kernel Hilbert space (RKHS), providing an analytic form for parameter estimation and a solid foundation for further theoretical analysis. The proposed model delivers a functional output predictive distribution derived analytically from a Bayesian perspective, enabling the quantification of uncertainty in the predicted function. We demonstrate the model's enhanced prediction performance through experiments on artificial datasets and density of states prediction tasks in materials science.

Forecasting the volatility of financial assets is essential for various financial applications. This paper addresses the challenging task of forecasting the volatility of financial assets with limited historical data, such as new issues or spin-offs, by proposing a multi-source transfer learning approach. Specifically, we exploit complementary source data of assets with a substantial historical data record by selecting source time series instances that are most similar to the limited target data of the new issue/spin-off. Based on these instances and the target data, we estimate linear and non-linear realized volatility models and compare their forecasting performance to forecasts of models trained exclusively on the target data, and models trained on the entire source and target data. The results show that our transfer learning approach outperforms the alternative models and that the integration of complementary data is also beneficial immediately after the initial trading day of the new issue/spin-off.

The scramjet engine is a key propulsion system for hypersonic vehicles, leveraging supersonic airflow to achieve high specific impulse, making it a promising technology for aerospace applications. Understanding and controlling the complex interactions between fuel injection, turbulent combustion, and aerodynamic effects of compressible flows are crucial for ensuring stable combustion in scramjet engines. However, identifying stable modes in scramjet combustors is often challenging due to limited experimental measurement means and extremely complex spatiotemporal evolution of supersonic turbulent combustion. This work introduces an innovative deep learning framework that combines dimensionality reduction via the Residual Convolutional Neural Network-beta-Variational Autoencoder (Res-CNN-beta-VAE) model with unsupervised clustering (K-means) to identify and analyze dynamical combustion modes in a supersonic combustor. By mapping high-dimensional data of combustion snapshots to a reduced three-dimensional latent space, the Res-CNN-beta-VAE model captures the essential temporal and spatial features of flame behaviors and enables the observation of transitions between combustion states. By analyzing the standard deviation of latent variable trajectories, we introduce a novel method for objectively distinguishing between dynamic transitions, which provides a scalable and expert-independent alternative to traditional classification methods. Besides, the unsupervised K-means clustering approach effectively identifies the complex interplay between the cavity and the jet-wake stabilization mechanisms, offering new insights into the system's behavior across different gas-to-liquid mass flow ratios (GLRs).

This paper proposes a model to predict the outcome of the March Madness tournament based on historical NCAA basketball data since 2013. The framework of this project is a simplification of the FiveThrityEight NCAA March Madness prediction model, where the only four predictors of interest are Adjusted Offensive Efficiency (ADJOE), Adjusted Defensive Efficiency (ADJDE), Power Rating, and Two-Point Shooting Percentage Allowed. A logistic regression was utilized with the aforementioned metrics to generate a probability of a particular team winning each game. Then, a tournament simulation is developed and compared to real-world March Madness brackets to determine the accuracy of the model. Accuracies of performance were calculated using a naive approach and a Spearman rank correlation coefficient.

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

Subjective interpretation and content diversity make predicting whether an image is private or public a challenging task. Graph neural networks combined with convolutional neural networks (CNNs), which consist of 14,000 to 500 millions parameters, generate features for visual entities (e.g., scene and object types) and identify the entities that contribute to the decision. In this paper, we show that using a simpler combination of transfer learning and a CNN to relate privacy with scene types optimises only 732 parameters while achieving comparable performance to that of graph-based methods. On the contrary, end-to-end training of graph-based methods can mask the contribution of individual components to the classification performance. Furthermore, we show that a high-dimensional feature vector, extracted with CNNs for each visual entity, is unnecessary and complexifies the model. The graph component has also negligible impact on performance, which is driven by fine-tuning the CNN to optimise image features for privacy nodes.

Constructing high resolution air pollution maps at lower cost is crucial for sustainable city management and public health risk assessment. However, traditional fixed-site monitoring lacks spatial coverage, while mobile low-cost sensors exhibit significant data instability. This study integrates PM2.5 data from 320 taxi-mounted mobile low-cost sensors and 52 fixed monitoring stations to address these limitations. By employing the machine learning methods, an appropriate mapping relationship was established between fixed and mobile monitoring concentration. The resulting pollution maps achieved 500-meter spatial and 5-minute temporal resolutions, showing close alignment with fixed monitoring data (+4.35% bias) but significant deviation from raw mobile data (-31.77%). The fused map exhibits the fine-scale spatial variability also observed in the mobile pollution map, while showing the stable temporal variability closer to that of the fixed pollution map (fixed: 1.12 plus or minus 0.73%, mobile: 3.15 plus or minus 2.44%, mapped: 1.01 plus or minus 0.65%). These findings demonstrate the potential of large-scale mobile low-cost sensor networks for high-resolution air quality mapping, supporting targeted urban environmental governance and health risk mitigation.