Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same self-symmetries as the input. This poses an important problem, both (1) for prediction tasks on domains where self-symmetries are common, and (2) for generative models, which must break symmetries in order to reconstruct from highly symmetric latent spaces. This fundamental limitation can be addressed by considering equivariant conditional distributions, instead of equivariant functions. We present novel theoretical results that establish necessary and sufficient conditions for representing such distributions. Concretely, this representation provides a practical framework for breaking symmetries in any equivariant network via randomized canonicalization. Our method, SymPE (Symmetry-breaking Positional Encodings), admits a simple interpretation in terms of positional encodings. This approach expands the representational power of equivariant networks while retaining the inductive bias of symmetry, which we justify through generalization bounds. Experimental results demonstrate that SymPE significantly improves performance of group-equivariant and graph neural networks across diffusion models for graphs, graph autoencoders, and lattice spin system modeling.

To build a motor system of the interactive avatar, it is essential to develop a generative motion model drives the body to move through 3D space in a perpetual, realistic, controllable, and responsive manner. Although motion generation has been extensively studied, most methods do not support ``embodied intelligence'' due to their offline setting, slow speed, limited motion lengths, or unnatural movements. To overcome these limitations, we propose PRIMAL, an autoregressive diffusion model that is learned with a two-stage paradigm, inspired by recent advances in foundation models. In the pretraining stage, the model learns motion dynamics from a large number of sub-second motion segments, providing ``motor primitives'' from which more complex motions are built. In the adaptation phase, we employ a ControlNet-like adaptor to fine-tune the motor control for semantic action generation and spatial target reaching. Experiments show that physics effects emerge from our training. Given a single-frame initial state, our model not only generates unbounded, realistic, and controllable motion, but also enables the avatar to be responsive to induced impulses in real time. In addition, we can effectively and efficiently adapt our base model to few-shot personalized actions and the task of spatial control. Evaluations show that our proposed method outperforms state-of-the-art baselines. We leverage the model to create a real-time character animation system in Unreal Engine that is highly responsive and natural. Code, models, and more results are available at: https://yz-cnsdqz.github.io/eigenmotion/PRIMAL

The digital twin edge network (DITEN) is a significant paradigm in the sixth-generation wireless system (6G) that aims to organize well-developed infrastructures to meet the requirements of evolving application scenarios. However, the impact of the interaction between the long-term DITEN maintenance and detailed digital twin tasks, which often entail privacy considerations, is commonly overlooked in current research. This paper addresses this issue by introducing a problem of digital twin association and historical data allocation for a federated learning (FL) task within DITEN. To achieve this goal, we start by introducing a closed-form function to predict the training accuracy of the FL task, referring to it as the data utility. Subsequently, we carry out comprehensive convergence analyses on the proposed FL methodology. Our objective is to jointly optimize the data utility of the digital twin-empowered FL task and the energy costs incurred by the long-term DITEN maintenance, encompassing FL model training, data synchronization, and twin migration. To tackle the aforementioned challenge, we present an optimization-driven learning algorithm that effectively identifies optimized solutions for the formulated problem. Numerical results demonstrate that our proposed algorithm outperforms various baseline approaches.

Abstract--Mobile Edge Computing (MEC) offers low-latency and high-bandwidth support for Internet-of-Vehicles (IoV) applications. However, due to high vehicle mobility and finite communication coverage of base stations, it is hard to maintain uninterrupted and high-quality services without proper service migration among MEC servers. Existing solutions commonly rely on prior knowledge and rarely consider efficient resource allocation during the service migration process, making it hard to reach optimal performance in dynamic IoV environments. To address these important challenges, we propose SR-CL, a novel mobility-aware seamless Service migration and Resource allocation framework via Convex-optimization-enabled deep reinforcement Learning in multi-edge IoV systems. First, we decouple the Mixed Integer Nonlinear Programming (MINLP) problem of service migration and resource allocation into two sub-problems. Next, we design a new actor-critic-based asynchronous-update deep reinforcement learning method to handle service migration, where the delayed-update actor makes migration decisions and the one-step-update critic evaluates the decisions to guide the policy update. Notably, we theoretically derive the optimal resource allocation with convex optimization for each MEC server, thereby further improving system performance. Using the real-world datasets of vehicle trajectories and testbed, extensive experiments are conducted to verify the effectiveness of the proposed SR-CL. Compared to benchmark methods, the SR-CL achieves superior convergence and delay performance under various scenarios. However, the real-time demands of IoV applications pose When vehicles offload tasks, MEC servers create dedicated significant challenges for onboard processors with limited service instances via virtualization techniques for the vehicles computational capabilities [2]. Although Cloud Computing and allocate proper resources to them [7].

Diabetes is a prevalent chronic disease with significant health and economic burdens worldwide. Early prediction and diagnosis can aid in effective management and prevention of complications. This study explores the use of machine learning models to predict diabetes based on lifestyle factors using data from the Behavioral Risk Factor Surveillance System (BRFSS) 2015 survey. The dataset consists of 21 lifestyle and health-related features, capturing aspects such as physical activity, diet, mental health, and socioeconomic status. Three classification models, Decision Tree, K-Nearest Neighbors (KNN), and Logistic Regression, are implemented and evaluated to determine their predictive performance. The models are trained and tested using a balanced dataset, and their performances are assessed based on accuracy, precision, recall, and F1-score. The results indicate that the Decision Tree, KNN, and Logistic Regression achieve an accuracy of 0.74, 0.72, and 0.75, respectively, with varying strengths in precision and recall. The findings highlight the potential of machine learning in diabetes prediction and suggest future improvements through feature selection and ensemble learning techniques.

Interpretability analysis methods for artificial intelligence models, such as LIME and SHAP, are widely used, though they primarily serve as post-model for analyzing model outputs. While it is commonly believed that the transparency and interpretability of AI models diminish as their complexity increases, currently there is no standardized method for assessing the inherent interpretability of the models themselves. This paper uses bond market default prediction as a case study, applying commonly used machine learning algorithms within AI models. First, the classification performance of these algorithms in default prediction is evaluated. Then, leveraging LIME and SHAP to assess the contribution of sample features to prediction outcomes, the paper proposes a novel method for evaluating the interpretability of the models themselves. The results of this analysis are consistent with the intuitive understanding and logical expectations regarding the interpretability of these models.

Generating novel molecules with out-of-distribution properties is a major challenge in molecular discovery. While supervised learning methods generate high-quality molecules similar to those in a dataset, they struggle to generalize to out-of-distribution properties. Reinforcement learning can explore new chemical spaces but often conducts 'reward-hacking' and generates non-synthesizable molecules. In this work, we address this problem by integrating a state-of-the-art supervised learning method, STGG+, in an active learning loop. Our approach iteratively generates, evaluates, and fine-tunes STGG+ to continuously expand its knowledge. We denote this approach STGG+AL. We apply STGG+AL to the design of organic $\pi$-functional materials, specifically two challenging tasks: 1) generating highly absorptive molecules characterized by high oscillator strength and 2) designing absorptive molecules with reasonable oscillator strength in the near-infrared (NIR) range. The generated molecules are validated and rationalized in-silico with time-dependent density functional theory. Our results demonstrate that our method is highly effective in generating novel molecules with high oscillator strength, contrary to existing methods such as reinforcement learning (RL) methods. We open-source our active-learning code along with our Conjugated-xTB dataset containing 2.9 million $\pi$-conjugated molecules and the function for approximating the oscillator strength and absorption wavelength (based on sTDA-xTB).

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper takes the first step toward a rigorous analysis of multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory. Code is available at: \url{https://github.com/ML-GSAI/Multi-Source-GM}.

The current generation of large language models (LLMs) is typically designed for broad, general-purpose applications, while domain-specific LLMs, especially in vertical fields like medicine, remain relatively scarce. In particular, the development of highly efficient and practical LLMs for the medical domain is challenging due to the complexity of medical knowledge and the limited availability of high-quality data. To bridge this gap, we introduce Baichuan-M1, a series of large language models specifically optimized for medical applications. Unlike traditional approaches that simply continue pretraining on existing models or apply post-training to a general base model, Baichuan-M1 is trained from scratch with a dedicated focus on enhancing medical capabilities. Our model is trained on 20 trillion tokens and incorporates a range of effective training methods that strike a balance between general capabilities and medical expertise. As a result, Baichuan-M1 not only performs strongly across general domains such as mathematics and coding but also excels in specialized medical fields. We have open-sourced Baichuan-M1-14B, a mini version of our model, which can be accessed through the following links.

Graph learning is a prevalent field that operates on ubiquitous graph data. Effective graph learning methods can extract valuable information from graphs. However, these methods are non-robust and affected by missing attributes in graphs, resulting in sub-optimal outcomes. This has led to the emergence of incomplete graph learning, which aims to process and learn from incomplete graphs to achieve more accurate and representative results. In this paper, we conducted a comprehensive review of the literature on incomplete graph learning. Initially, we categorize incomplete graphs and provide precise definitions of relevant concepts, terminologies, and techniques, thereby establishing a solid understanding for readers. Subsequently, we classify incomplete graph learning methods according to the types of incompleteness: (1) attribute-incomplete graph learning methods, (2) attribute-missing graph learning methods, and (3) hybrid-absent graph learning methods. By systematically classifying and summarizing incomplete graph learning methods, we highlight the commonalities and differences among existing approaches, aiding readers in selecting methods and laying the groundwork for further advancements. In addition, we summarize the datasets, incomplete processing modes, evaluation metrics, and application domains used by the current methods. Lastly, we discuss the current challenges and propose future directions for incomplete graph learning, with the aim of stimulating further innovations in this crucial field. To our knowledge, this is the first review dedicated to incomplete graph learning, aiming to offer valuable insights for researchers in related fields.We developed an online resource to follow relevant research based on this review, available at https://github.com/cherry-a11y/Incomplete-graph-learning.git