Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems. For strongly convex optimization problems or strongly monotone games, these results provide tracking guarantees under the assumption that the variation of the time-varying problem is restrained, that is, problems with a sublinear solution path. In this work we extend existing results in two ways: In our first result, we provide tracking bounds for (1) variational inequalities with a sublinear solution path but not necessarily monotone functions, and (2) for periodic time-varying variational inequalities that do not necessarily have a sublinear solution path-length. Our second main contribution is an extensive study of the convergence behavior and trajectory of discrete dynamical systems of periodic time-varying VI. We show that these systems can exhibit provably chaotic behavior or can converge to the solution. Finally, we illustrate our theoretical results with experiments.

Global Station Weather Forecasting (GSWF) is crucial for various sectors, including aviation, agriculture, energy, and disaster preparedness. Recent advancements in deep learning have significantly improved the accuracy of weather predictions by optimizing models based on public meteorological data. However, existing public datasets for GSWF optimization and benchmarking still suffer from significant limitations, such as small sizes, limited temporal coverage, and a lack of comprehensive variables. These shortcomings prevent them from effectively reflecting the benchmarks of current forecasting methods and fail to support the real needs of operational weather forecasting. To address these challenges, we present the WEATHER-5K dataset. This dataset comprises a comprehensive collection of data from 5,672 weather stations worldwide, spanning a 10-year period with one-hour intervals. It includes multiple crucial weather elements, providing a more reliable and interpretable resource for forecasting. Furthermore, our WEATHER-5K dataset can serve as a benchmark for comprehensively evaluating existing well-known forecasting models, extending beyond GSWF methods to support future time-series research challenges and opportunities.

Fair supervised learning algorithms assigning labels with little dependence on a sensitive attribute have attracted great attention in the machine learning community. While the demographic parity (DP) notion has been frequently used to measure a model's fairness in training fair classifiers, several studies in the literature suggest potential impacts of enforcing DP in fair learning algorithms. In this work, we analytically study the effect of standard DP-based regularization methods on the conditional distribution of the predicted label given the sensitive attribute. Our analysis shows that an imbalanced training dataset with a non-uniform distribution of the sensitive attribute could lead to a classification rule biased toward the sensitive attribute outcome holding the majority of training data. To control such inductive biases in DP-based fair learning, we propose a sensitive attribute-based distributionally robust optimization (SA-DRO) method improving robustness against the marginal distribution of the sensitive attribute. Finally, we present several numerical results on the application of DP-based learning methods to standard centralized and distributed learning problems. The empirical findings support our theoretical results on the inductive biases in DP-based fair learning algorithms and the debiasing effects of the proposed SA-DRO method.

The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in human evolutionary history, it has been suggested that LMS processing may build upon more fundamental cognitive systems, possibly through neuronal recycling. Previous studies have pinpointed two primary candidates, natural language processing and spatial cognition. Existing comparisons between these domains largely relied on task-level comparison, which may be confounded by task idiosyncrasy. The present study instead compared the neural correlates at the domain level with both automated meta-analysis and synthesized maps based on three representative LMS tasks, reasoning, calculation, and mental programming. Our results revealed a more substantial cortical overlap between LMS processing and spatial cognition, in contrast to language processing. Furthermore, in regions activated by both spatial and language processing, the multivariate activation pattern for LMS processing exhibited greater multivariate similarity to spatial cognition than to language processing. A hierarchical clustering analysis further indicated that typical LMS tasks were indistinguishable from spatial cognition tasks at the neural level, suggesting an inherent connection between these two cognitive processes. Taken together, our findings support the hypothesis that spatial cognition is likely the basis of LMS processing, which may shed light on the limitations of large language models in logical reasoning, particularly those trained exclusively on textual data without explicit emphasis on spatial content.

Machine unlearning facilitates personal data ownership, including the ``right to be forgotten''. The proliferation of applications of \emph{neural networks} (NNs) trained on users' personal data calls for the need to develop algorithms to unlearn an NN. Since retraining is costly, efficiency is often achieved through approximate unlearning which aims to unlearn a trained NN to be close to the retrained one (in distribution). Though the Newton's method has been used by previous works to approximately unlearn linear models, adapting it for unlearning an NN often encounters degenerate Hessians that make computing the Newton's update impossible. In this paper, we will first show that when coupled with naive yet often effective solutions to mitigate the degeneracy issue for unlearning, the Newton's method surprisingly suffers from catastrophic forgetting. To overcome this difficulty, we revise the Newton's method to include a theoretically justified regularizer and propose a cubic-regularized Newton's method for unlearning an NN. The cubic regularizer comes with the benefits of not requiring manual finetuning and affording a natural interpretation. Empirical evaluation on several models and real-world datasets shows that our method is more resilient to catastrophic forgetting and performs better than the baselines, especially in sequential unlearning.

LLMs offer valuable capabilities, yet they can be utilized by malicious users to disseminate deceptive information and generate fake news. The growing prevalence of LLMs poses difficulties in crafting detection approaches that remain effective across various text domains. Additionally, the absence of precautionary measures for AI-generated news on online social platforms is concerning. Therefore, there is an urgent need to improve people's ability to differentiate between news articles written by humans and those produced by LLMs. By providing cues in human-written and LLM-generated news, we can help individuals increase their skepticism towards fake LLM-generated news. This paper aims to elucidate simple markers that help individuals distinguish between articles penned by humans and those created by LLMs. To achieve this, we initially collected a dataset comprising 39k news articles authored by humans or generated by four distinct LLMs with varying degrees of fake. We then devise a metric named Entropy-Shift Authorship Signature (ESAS) based on the information theory and entropy principles. The proposed ESAS ranks terms or entities, like POS tagging, within news articles based on their relevance in discerning article authorship. We demonstrate the effectiveness of our metric by showing the high accuracy attained by a basic method, i.e., TF-IDF combined with logistic regression classifier, using a small set of terms with the highest ESAS score. Consequently, we introduce and scrutinize these top ESAS-ranked terms to aid individuals in strengthening their skepticism towards LLM-generated fake news.

Federated learning is highly susceptible to model poisoning attacks, especially those meticulously crafted for servers. Traditional defense methods mainly focus on updating assessments or robust aggregation against manually crafted myopic attacks. When facing advanced attacks, their defense stability is notably insufficient. Therefore, it is imperative to develop adaptive defenses against such advanced poisoning attacks. We find that benign clients exhibit significantly higher data distribution stability than malicious clients in federated learning in both CV and NLP tasks. Therefore, the malicious clients can be recognized by observing the stability of their data distribution. In this paper, we propose AdaAggRL, an RL-based Adaptive Aggregation method, to defend against sophisticated poisoning attacks. Specifically, we first utilize distribution learning to simulate the clients' data distributions. Then, we use the maximum mean discrepancy (MMD) to calculate the pairwise similarity of the current local model data distribution, its historical data distribution, and global model data distribution. Finally, we use policy learning to adaptively determine the aggregation weights based on the above similarities. Experiments on four real-world datasets demonstrate that the proposed defense model significantly outperforms widely adopted defense models for sophisticated attacks.

The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent complexity posed implementation challenges. Consequently, researchers have explored alternative basis functions such as Wavelets, Polynomials, and Fractional functions. In this research, we explore the use of rational functions as a novel basis function for KANs. We propose two different approaches based on Pade approximation and rational Jacobi functions as trainable basis functions, establishing the rational KAN (rKAN). We then evaluate rKAN's performance in various deep learning and physics-informed tasks to demonstrate its practicality and effectiveness in function approximation.

When data are right-censored, i.e. some outcomes are missing due to a limited period of observation, survival analysis can compute the "time to event". Multiple classes of outcomes lead to a classification variant: predicting the most likely event, known as competing risks, which has been less studied. To build a loss that estimates outcome probabilities for such settings, we introduce a strictly proper censoring-adjusted separable scoring rule that can be optimized on a subpart of the data because the evaluation is made independently of observations. It enables stochastic optimization for competing risks which we use to train gradient boosting trees. Compared to 11 state-of-the-art models, this model, MultiIncidence, performs best in estimating the probability of outcomes in survival and competing risks. It can predict at any time horizon and is much faster than existing alternatives.

Cohort studies are of significant importance in the field of healthcare analysis. However, existing methods typically involve manual, labor-intensive, and expert-driven pattern definitions or rely on simplistic clustering techniques that lack medical relevance. Automating cohort studies with interpretable patterns has great potential to facilitate healthcare analysis but remains an unmet need in prior research efforts. In this paper, we propose a cohort auto-discovery model, CohortNet, for interpretable healthcare analysis, focusing on the effective identification, representation, and exploitation of cohorts characterized by medically meaningful patterns. CohortNet initially learns fine-grained patient representations by separately processing each feature, considering both individual feature trends and feature interactions at each time step. Subsequently, it classifies each feature into distinct states and employs a heuristic cohort exploration strategy to effectively discover substantial cohorts with concrete patterns. For each identified cohort, it learns comprehensive cohort representations with credible evidence through associated patient retrieval. Ultimately, given a new patient, CohortNet can leverage relevant cohorts with distinguished importance, which can provide a more holistic understanding of the patient's conditions. Extensive experiments on three real-world datasets demonstrate that it consistently outperforms state-of-the-art approaches and offers interpretable insights from diverse perspectives in a top-down fashion.