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The emergence of Large Language Models (LLMs), has opened exciting possibilities for constructing computational simulations designed to replicate human behavior accurately. Current research suggests that LLM-based agents become increasingly human-like in their performance, sparking interest in using these AI agents as substitutes for human participants in behavioral studies. However, LLMs are complex statistical learners without straightforward deductive rules, making them prone to unexpected behaviors. Hence, it is crucial to study and pinpoint the key behavioral distinctions between humans and LLM-based agents. In this study, we highlight the limitations of LLMs in simulating human interactions, particularly focusing on LLMs' ability to simulate political debates on topics that are important aspects of people's day-to-day lives and decision-making processes. Our findings indicate a tendency for LLM agents to conform to the model's inherent social biases despite being directed to debate from certain political perspectives. This tendency results in behavioral patterns that seem to deviate from well-established social dynamics among humans. We reinforce these observations using an automatic self-fine-tuning method, which enables us to manipulate the biases within the LLM and demonstrate that agents subsequently align with the altered biases. These results underscore the need for further research to develop methods that help agents overcome these biases, a critical step toward creating more realistic simulations.

Online learning of deep neural networks suffers from challenges such as hysteretic non-incremental updating, increasing memory usage, past retrospective retraining, and catastrophic forgetting. To alleviate these drawbacks and achieve progressive immediate decision-making, we propose a novel Incremental Online Learning (IOL) process of Randomized Neural Networks (Randomized NN), a framework facilitating continuous improvements to Randomized NN performance in restrictive online scenarios. Within the framework, we further introduce IOL with ridge regularization (-R) and IOL with forward regularization (-F). -R generates stepwise incremental updates without retrospective retraining and avoids catastrophic forgetting. Moreover, we substituted -R with -F as it enhanced precognition learning ability using semi-supervision and realized better online regrets to offline global experts compared to -R during IOL. The algorithms of IOL for Randomized NN with -R/-F on non-stationary batch stream were derived respectively, featuring recursive weight updates and variable learning rates. Additionally, we conducted a detailed analysis and theoretically derived relative cumulative regret bounds of the Randomized NN learners with -R/-F in IOL under adversarial assumptions using a novel methodology and presented several corollaries, from which we observed the superiority on online learning acceleration and regret bounds of employing -F in IOL. Finally, our proposed methods were rigorously examined across regression and classification tasks on diverse datasets, which distinctly validated the efficacy of IOL frameworks of Randomized NN and the advantages of forward regularization.

Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure reliability. However, there is still a relative lack of systematic assessment of the uncertainties, particularly the uncertainties of the physical data. Our motivation is to introduce conformal prediction into the uncertainty assessment of dynamical systems, providing a method supported by theoretical guarantees. This paper uses the conformal prediction method to assess uncertainties with benchmark operator learning methods. We have also compared the Monte Carlo Dropout and Ensemble methods in the partial differential equations dataset, effectively evaluating uncertainty through straight roll-outs, making it ideal for time-series tasks.

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional data in two dimensions to enable visual exploration. However, popular embedding techniques, such as t-SNE and UMAP, typically assume that data points are independent. When this assumption is violated, as in time-series data, the resulting visualizations may fail to reveal important temporal patterns and trends. To address this, we propose a formal extension to existing dimensionality reduction methods that incorporates two temporal loss terms that explicitly highlight temporal progression in the embedded visualizations. Through a series of experiments on both synthetic and real-world datasets, we demonstrate that our approach effectively uncovers temporal patterns and improves the interpretability of the visualizations. Furthermore, the method improves temporal coherence while preserving the fidelity of the embeddings, providing a robust tool for dynamic data analysis.

Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by showing that an aperiodic monotile exists in sufficiently high dimension $n$ [Ann. Math. 200(2024), 301-363]. In another paper [to appear in J. Eur. Math. Soc.], they also show that if the dimension $n$ is part of the input, then the translational tiling for subsets of $\mathbb{Z}^n$ with one tile is undecidable. These two results are very strong pieces of evidence for the conjecture that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable, for some fixed $n$. This paper gives another supportive result for this conjecture by showing that translational tiling of the $4$-dimensional space with a set of three connected tiles is undecidable.

The study of biomechanics during locomotion provides valuable insights into the effects of varying conditions on specific movement patterns. This research focuses on examining the influence of different shoe parameters on walking biomechanics, aiming to understand their impact on gait patterns. To achieve this, various methodologies are explored to estimate human body biomechanics, including computer vision techniques and wearable devices equipped with advanced sensors. Given privacy considerations and the need for robust, accurate measurements, this study employs wearable devices with Inertial Measurement Unit (IMU) sensors. These devices offer a non-invasive, precise, and high-resolution approach to capturing biomechanical data during locomotion. Raw sensor data collected from wearable devices is processed using an Extended Kalman Filter to reduce noise and extract meaningful information. This includes calculating joint angles throughout the gait cycle, enabling a detailed analysis of movement dynamics. The analysis identifies correlations between shoe parameters and key gait characteristics, such as stability, mobility, step time, and propulsion forces. The findings provide deeper insights into how footwear design influences walking efficiency and biomechanics. This study paves the way for advancements in footwear technology and contributes to the development of personalized solutions for enhancing gait performance and mobility.

The success of AI models relies on the availability of large, diverse, and high-quality datasets, which can be challenging to obtain due to data scarcity, privacy concerns, and high costs. Synthetic data has emerged as a promising solution by generating artificial data that mimics real-world patterns. This paper provides an overview of synthetic data research, discussing its applications, challenges, and future directions. We present empirical evidence from prior art to demonstrate its effectiveness and highlight the importance of ensuring its factuality, fidelity, and unbiasedness. We emphasize the need for responsible use of synthetic data to build more powerful, inclusive, and trustworthy language models.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.