Dataset distances provide a powerful framework for comparing datasets based on their underlying structures, distributions, or content. These measures are essential in applications where understanding the relationships between datasets drives decision-making, such as assessing data quality, detecting distributional shifts, or quantifying biases. They play a critical role in machine learning workflows, enabling tasks like domain adaptation, transfer learning, continual learning, and fairness evaluation. Additionally, dataset distances are valuable in emerging areas such as synthetic data evaluation, 3D shape comparison, and federated learning, where comparing heterogeneous data distributions is fundamental. By capturing meaningful similarities and differences between datasets, these measures facilitate data-driven insights, enhance model robustness, and support novel applications across diverse fields. A common approach to comparing datasets relies on proxies, such as analyzing the learning curves of a predefined model [28, 16] or examining its optimal parameters [1, 22] on a given task. Another strategy involves making strong assumptions about the similarity or co-occurrence of labels between datasets [47]. However, these methods often lack theoretical guarantees, are heavily dependent on the choice of the probe model, and require training the model to completion (e.g., to identify optimal parameters) for each dataset under comparison. To address limitations of previous approaches, model-agnostic approaches are developed.

Akeylimitationofthesemodels,however,istheirrelianceon a fixed time horizon, which introduces an artificial time dependency in the drift function of the backward process. As a result, the generative denoising process follows a predefined number of steps, regardless of the actual level of noise present along the generated path. To overcome this limitation, we introduce a novel class of diffusion models that dynamically adapt to the state of the denoising process. By replacing the fixed deterministic time horizon with a random one and conditioning the forward process to terminate at a predefined target distribution, our approach achieves greater flexibility and state awareness. The foundation of our method lies in Doob's h-transforms with respect to underlying exponential times. While the theoretical groundwork for this concept exists, its explicit application and detailed exploration - particularly in comparison to deterministic time horizons - remains underrepresented in the literature. A key feature of our model is its inherent adaptability: the number of denoising steps dynamically adjusts based on the noise level in the data, introducing a stochastic element. This randomness not only enhances the generation process, but also allows denoising to start from partially noisy data, naturally incorporating conditioning.

Big data, both in its structured and unstructured formats, have brought in unforeseen challenges in economics and business. How to organize, classify, and then analyze such data to obtain meaningful insights are the ever-going research topics for business leaders and academic researchers. This paper studies recent applications of deep neural networks in decision making in economical business and investment; especially in risk management, portfolio optimization, and algorithmic trading. Set aside limitation in data privacy and cross-market analysis, the article establishes that deep neural networks have performed remarkably in financial classification and prediction. Moreover, the study suggests that by compositing multiple neural networks, spanning different data type modalities, a more robust, efficient, and scalable financial prediction framework can be constructed.

Efficient job allocation in complex scheduling problems poses significant challenges in real-world applications. In this report, we propose a novel approach that leverages the power of Reinforcement Learning (RL) and Graph Neural Networks (GNNs) to tackle the Job Allocation Problem (JAP). The JAP involves allocating a maximum set of jobs to available resources while considering several constraints. Our approach enables learning of adaptive policies through trial-and-error interactions with the environment while exploiting the graph-structured data of the problem. By leveraging RL, we eliminate the need for manual annotation, a major bottleneck in supervised learning approaches. Experimental evaluations on synthetic and real-world data demonstrate the effectiveness and generalizability of our proposed approach, outperforming baseline algorithms and showcasing its potential for optimizing job allocation in complex scheduling problems.

With the rise in global greenhouse gas emissions, accurate large-scale tree canopy height maps are essential for understanding forest structure, estimating above-ground biomass, and monitoring ecological disruptions. To this end, we present a novel approach to generate large-scale, high-resolution canopy height maps over time. Our model accurately predicts canopy height over multiple years given Sentinel-2 time series satellite data. Using GEDI LiDAR data as the ground truth for training the model, we present the first 10m resolution temporal canopy height map of the European continent for the period 2019-2022. As part of this product, we also offer a detailed canopy height map for 2020, providing more precise estimates than previous studies. Our pipeline and the resulting temporal height map are publicly available, enabling comprehensive large-scale monitoring of forests and, hence, facilitating future research and ecological analyses. For an interactive viewer, see https://europetreemap.projects.earthengine.app/view/temporalcanopyheight.

Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at hand, subsequent mathematical formulation, and numerical approximation. Data-driven models instead aim to extract relations between input and output data without arguing any causality principle underlining the available data distribution. In recent years, data-driven models have been rapidly developed and popularized. Such a diffusion has been triggered by a huge availability of data (the so-called big data), an increasingly cheap computing power, and the development of powerful machine learning algorithms. SciML leverages the physical awareness of physics-based models and, at the same time, the efficiency of data-driven algorithms. With SciML, we can inject physics and mathematical knowledge into machine learning algorithms. Yet, we can rely on data-driven algorithms' capability to discover complex and non-linear patterns from data and improve the descriptive capacity of physics-based models. After recalling the mathematical foundations of digital modelling and machine learning algorithms, and presenting the most popular machine learning architectures, we discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by partial differential equations. Finally, we illustrate the successful application of SciML to the simulation of the human cardiac function, a field of significant socio-economic importance that poses numerous challenges on both the mathematical and computational fronts. The corresponding mathematical model is a complex system of non-linear ordinary and partial differential equations describing the electromechanics, valve dynamics, blood circulation, perfusion in the coronary tree, and torso potential. Despite the robustness and accuracy of physics-based models, certain aspects, such as unveiling constitutive laws for cardiac cells and myocardial material properties, as well as devising efficient reduced order models to dominate the extraordinary computational complexity, have been successfully tackled by leveraging data-driven models.

In this work, we dive into the fundamental challenges of evaluating Text2SQL solutions and highlight potential failure causes and the potential risks of relying on aggregate metrics in existing benchmarks. We identify two largely unaddressed limitations in current open benchmarks: (1) data quality issues in the evaluation data, mainly attributed to the lack of capturing the probabilistic nature of translating a natural language description into a structured query (e.g., NL ambiguity), and (2) the bias introduced by using different match functions as approximations for SQL equivalence. To put both limitations into context, we propose a unified taxonomy of all Text2SQL limitations that can lead to both prediction and evaluation errors. We then motivate the taxonomy by providing a survey of Text2SQL limitations using state-of-the-art Text2SQL solutions and benchmarks. We describe the causes of limitations with real-world examples and propose potential mitigation solutions for each category in the taxonomy. We conclude by highlighting the open challenges encountered when deploying such mitigation strategies or attempting to automatically apply the taxonomy.

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets time-series data as \textit{discrete samples from an underlying continuous dynamical system}, and models its time evolution using Neural Stochastic Differential Equation (Neural SDE), where both the flow (drift) and diffusion terms are parameterized by neural networks. We derive a principled maximum likelihood objective and a \textit{simulation-free} scheme for efficient training of our Neural SDE model. We demonstrate the versatility of our approach through experiments on sequence modeling tasks across both embodied and generative AI. Notably, to the best of our knowledge, this is the first work to show that SDE-based continuous-time modeling also excels in such complex scenarios, and we hope that our work opens up new avenues for research of SDE models in high-dimensional and temporally intricate domains.

The increasing size and complexity of pre-trained language models have demonstrated superior performance in many applications, but they usually require large training datasets to be adequately trained. Insufficient training sets could unexpectedly make the model overfit and fail to cope with complex tasks. Large language models (LLMs) trained on extensive corpora have prominent text generation capabilities, which improve the quality and quantity of data and play a crucial role in data augmentation. Specifically, distinctive prompt templates are given in personalised tasks to guide LLMs in generating the required content. Recent promising retrieval-based techniques further improve the expressive performance of LLMs in data augmentation by introducing external knowledge to enable them to produce more grounded-truth data. This survey provides an in-depth analysis of data augmentation in LLMs, classifying the techniques into Simple Augmentation, Prompt-based Augmentation, Retrieval-based Augmentation and Hybrid Augmentation. We summarise the post-processing approaches in data augmentation, which contributes significantly to refining the augmented data and enabling the model to filter out unfaithful content. Then, we provide the common tasks and evaluation metrics. Finally, we introduce existing challenges and future opportunities that could bring further improvement to data augmentation.

Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based sampler known for its practical efficiency. While a number of prior works address its general convergence theory, it remains unclear whether the probability flow ODE sampler can adapt to the low-dimensional structures commonly present in natural image data. We demonstrate that, with accurate score function estimation, the probability flow ODE sampler achieves a convergence rate of $O(k/T)$ in total variation distance (ignoring logarithmic factors), where $k$ is the intrinsic dimension of the target distribution and $T$ is the number of iterations. This dimension-free convergence rate improves upon existing results that scale with the typically much larger ambient dimension, highlighting the ability of the probability flow ODE sampler to exploit intrinsic low-dimensional structures in the target distribution for faster sampling.