Neural operators, particularly the Deep Operator Network (DeepONet), have shown promise in learning mappings between function spaces for solving differential equations. However, standard DeepONet requires input functions to be sampled at fixed locations, limiting its applicability when sensor configurations vary or inputs exist on irregular grids. We introduce the Set Operator Network (SetONet), which modifies DeepONet's branch network to process input functions as unordered sets of location-value pairs. By incorporating Deep Sets principles, SetONet ensures permutation invariance while maintaining the same parameter count as the baseline. On classical operator-learning benchmarks, SetONet achieves parity with DeepONet on fixed layouts while sustaining accuracy under variable sensor configurations or sensor drop-off - conditions for which standard DeepONet is not applicable. More significantly, SetONet natively handles problems where inputs are naturally represented as unstructured point clouds (such as point sources or density samples) rather than values on fixed grids, a capability standard DeepONet lacks. On heat conduction with point sources, advection-diffusion modeling chemical plumes, and optimal transport between density samples, SetONet learns operators end-to-end without rasterization or multi-stage pipelines. These problems feature inputs that are naturally discrete point sets (point sources or density samples) rather than functions on fixed grids. SetONet is a DeepONet-class architecture that addresses such problems with a lightweight design, significantly broadening the applicability of operator learning to problems with variable, incomplete, or unstructured input data.

Analyzing multi-featured time series data is critical for space missions making efficient event detection, potentially onboard, essential for automatic analysis. However, limited onboard computational resources and data downlink constraints necessitate robust methods for identifying regions of interest in real time. This work presents an adaptive outlier detection algorithm based on the reconstruction error of Principal Component Analysis (PCA) for feature reduction, designed explicitly for space mission applications. The algorithm adapts dynamically to evolving data distributions by using Incremental PCA, enabling deployment without a predefined model for all possible conditions. A pre-scaling process normalizes each feature's magnitude while preserving relative variance within feature types. We demonstrate the algorithm's effectiveness in detecting space plasma events, such as distinct space environments, dayside and nightside transients phenomena, and transition layers through NASA's MMS mission observations. Additionally, we apply the method to NASA's THEMIS data, successfully identifying a dayside transient using onboard-available measurements.

Federated learning (FL) is now recognized as a key framework for communication-efficient collaborative learning. Most theoretical and empirical studies, however, rely on the assumption that clients have access to pre-collected data sets, with limited investigation into scenarios where clients continuously collect data. In many real-world applications, particularly when data is generated by physical or biological processes, client data streams are often modeled by non-stationary Markov processes. Unlike standard i.i.d. sampling, the performance of FL with Markovian data streams remains poorly understood due to the statistical dependencies between client samples over time. In this paper, we investigate whether FL can still support collaborative learning with Markovian data streams. Specifically, we analyze the performance of Minibatch SGD, Local SGD, and a variant of Local SGD with momentum. We answer affirmatively under standard assumptions and smooth non-convex client objectives: the sample complexity is proportional to the inverse of the number of clients with a communication complexity comparable to the i.i.d. scenario. However, the sample complexity for Markovian data streams remains higher than for i.i.d. sampling.

\kmeans clustering is a fundamental problem in many scientific and engineering domains. The optimization problem associated with \kmeans clustering is nonconvex, for which standard algorithms are only guaranteed to find a local optimum. Leveraging the hidden structure of local solutions, we propose a general algorithmic framework for escaping undesirable local solutions and recovering the global solution or the ground truth clustering. This framework consists of iteratively alternating between two steps: (i) detect mis-specified clusters in a local solution, and (ii) improve the local solution by non-local operations. We discuss specific implementation of these steps, and elucidate how the proposed framework unifies many existing variants of \kmeans algorithms through a geometric perspective. We also present two natural variants of the proposed framework, where the initial number of clusters may be over- or under-specified. We provide theoretical justifications and extensive experiments to demonstrate the efficacy of the proposed approach.

Developing effective multimodal fusion approaches has become increasingly essential in many real-world scenarios, such as health care and finance. The key challenge is how to preserve the feature expressiveness in each modality while learning cross-modal interactions. Previous approaches primarily focus on the cross-modal alignment, while over-emphasis on the alignment of marginal distributions of modalities may impose excess regularization and obstruct meaningful representations within each modality. The Dirichlet process (DP) mixture model is a powerful Bayesian non-parametric method that can amplify the most prominent features by its richer-gets-richer property, which allocates increasing weights to them. Inspired by this unique characteristic of DP, we propose a new DP-driven multimodal learning framework that automatically achieves an optimal balance between prominent intra-modal representation learning and cross-modal alignment. Specifically, we assume that each modality follows a mixture of multivariate Gaussian distributions and further adopt DP to calculate the mixture weights for all the components. This paradigm allows DP to dynamically allocate the contributions of features and select the most prominent ones, leveraging its richer-gets-richer property, thus facilitating multimodal feature fusion. Extensive experiments on several multimodal datasets demonstrate the superior performance of our model over other competitors. Ablation analysis further validates the effectiveness of DP in aligning modality distributions and its robustness to changes in key hyperparameters. Code is anonymously available at https://github.com/HKU-MedAI/DPMM.git

In this study we aim to better align fall risk prediction from the Johns Hopkins Fall Risk Assessment Tool (JHFRAT) with additional clinically meaningful measures via a data-driven modelling approach. We conducted a retrospective analysis of 54,209 inpatient admissions from three Johns Hopkins Health System hospitals between March 2022 and October 2023. A total of 20,208 admissions were included as high fall risk encounters, and 13,941 were included as low fall risk encounters. To incorporate clinical knowledge and maintain interpretability, we employed constrained score optimization (CSO) models on JHFRAT assessment data and additional electronic health record (EHR) variables. The model demonstrated significant improvements in predictive performance over the current JHFRAT (CSO AUC-ROC=0.91, JHFRAT AUC-ROC=0.86). The constrained score optimization models performed similarly with and without the EHR variables. Although the benchmark black-box model (XGBoost), improves upon the performance metrics of the knowledge-based constrained logistic regression (AUC-ROC=0.94), the CSO demonstrates more robustness to variations in risk labelling. This evidence-based approach provides a robust foundation for health systems to systematically enhance inpatient fall prevention protocols and patient safety using data-driven optimization techniques, contributing to improved risk assessment and resource allocation in healthcare settings.

The ability to continually learn, retain and deploy skills to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of skills remain elusive. Here, we study continual learning and the compositional reuse of learned computations in recurrent neural network (RNN) models using a novel two-system approach: one system that infers what computation to perform, and one that implements how to perform it. We focus on a set of compositional cognitive tasks commonly studied in neuroscience. To construct the what system, we first show that a large family of tasks can be systematically described by a probabilistic generative model, where compositionality stems from a shared underlying vocabulary of discrete task epochs. The shared epoch structure makes these tasks inherently compositional. We first show that this compositionality can be systematically described by a probabilistic generative model. Furthermore, We develop an unsupervised online learning approach that can learn this model on a single-trial basis, building its vocabulary incrementally as it is exposed to new tasks, and inferring the latent epoch structure as a time-varying computational context within a trial. We implement the how system as an RNN whose low-rank components are composed according to the context inferred by the what system. Contextual inference facilitates the creation, learning, and reuse of low-rank RNN components as new tasks are introduced sequentially, enabling continual learning without catastrophic forgetting. Using an example task set, we demonstrate the efficacy and competitive performance of this two-system learning framework, its potential for forward and backward transfer, as well as fast compositional generalization to unseen tasks.

Minimum Bayes Risk (MBR) decoding has seen renewed interest as an alternative to traditional generation strategies. While MBR has proven effective in machine translation, where the variability of a language model's outcome space is naturally constrained, it may face challenges in more open-ended tasks such as dialogue or instruction-following. We hypothesise that in such settings, applying MBR with standard similarity-based utility functions may result in selecting responses that are broadly representative of the model's distribution, yet sub-optimal with respect to any particular grouping of generations that share an underlying latent structure. In this work, we introduce three lightweight adaptations to the utility function, designed to make MBR more sensitive to structural variability in the outcome space. To test our hypothesis, we curate a dataset capturing three representative types of latent structure: dialogue act, emotion, and response structure (e.g., a sentence, a paragraph, or a list). We further propose two metrics to evaluate the structural optimality of MBR. Our analysis demonstrates that common similarity-based utility functions fall short by these metrics. In contrast, our proposed adaptations considerably improve structural optimality. Finally, we evaluate our approaches on real-world instruction-following benchmarks, AlpacaEval and MT-Bench, and show that increased structural sensitivity improves generation quality by up to 13.7 percentage points in win rate.

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are dominated by graph-based proxies that quantify structural connectivity but do not clarify what constitutes high-quality reasoning; such abstractions can be overly simplistic for inherently complex processes. We introduce a topological data analysis (TDA)-based evaluation framework that captures the geometry of reasoning traces and enables label-efficient, automated assessment. In our empirical study, topological features yield substantially higher predictive power for assessing reasoning quality than standard graph metrics, suggesting that effective reasoning is better captured by higher-dimensional geometric structures rather than purely relational graphs. We further show that a compact, stable set of topological features reliably indicates trace quality, offering a practical signal for future reinforcement learning algorithms.

Abstract--Extreme events frequently occur in real-world time series and often carry significant practical implications. In domains such as climate and healthcare, these events, such as floods, heatwaves, or acute medical episodes, can lead to serious consequences. Accurate forecasting of such events is therefore of substantial importance. Most existing time series forecasting models are optimized for overall performance within the prediction window, but often struggle to accurately predict extreme events, such as high temperatures or heart rate spikes. The main challenges are data imbalance and the neglect of valuable information contained in intermediate events that precede extreme events. In this paper, we propose xTime, a novel framework for extreme event forecasting in time series. In addition, we introduce a mixture of experts (MoE) mechanism that dynamically selects and fuses outputs from expert models across different rarity levels, which further improves the forecasting performance for extreme events. Experiments on multiple datasets show that xTime achieves consistent improvements, with forecasting accuracy on extreme events improving from 3% to 78%. Time series forecasting plays a fundamental role across a broad spectrum of critical applications, such as stock market analysis, weather and climate modeling, and electricity demand prediction.