Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous optimization problem by characterizing the DAG constraint as a smooth equality one, generally based on polynomials over adjacency matrices. Existing methods place very small coefficients on high-order polynomial terms for stabilization, since they argue that large coefficients on the higher-order terms are harmful due to numeric exploding. On the contrary, we discover that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher-order terms can approximate the DAG constraints much better than the small counterparts. Based on this, we propose a novel DAG learning method with efficient truncated matrix power iteration to approximate geometric series based DAG constraints. Empirically, our DAG learning method outperforms the previous state-of-the-arts in various settings, often by a factor of $3$ or more in terms of structural Hamming distance.

The home space for optimal control is a Sobolev space. The home space for pseudospectral theory is also a Sobolev space. It thus seems natural to combine pseudospectral theory with optimal control theory and construct ``pseudospectral optimal control theory,'' a term coined by Ross. In this paper, we review key theoretical results in pseudospectral optimal control that have proven to be critical for a successful flight. Implementation details of flight demonstrations onboard NASA spacecraft are discussed along with emerging trends and techniques in both theory and practice. The 2011 launch of pseudospectral optimal control in embedded platforms is changing the way in which we see solutions to challenging control problems in aerospace and autonomous systems.

Evolutionary multitasking (EMT) algorithms typically require tailored designs for knowledge transfer, in order to assure convergence and optimality in multitask optimization. In this paper, we explore designing a systematic and generalizable knowledge transfer policy through Reinforcement Learning. We first identify three major challenges: determining the task to transfer (where), the knowledge to be transferred (what) and the mechanism for the transfer (how). To address these challenges, we formulate a multi-role RL system where three (groups of) policy networks act as specialized agents: a task routing agent incorporates an attention-based similarity recognition module to determine source-target transfer pairs via attention scores; a knowledge control agent determines the proportion of elite solutions to transfer; and a group of strategy adaptation agents control transfer strength by dynamically controlling hyper-parameters in the underlying EMT framework. Through pre-training all network modules end-to-end over an augmented multitask problem distribution, a generalizable meta-policy is obtained. Comprehensive validation experiments show state-of-the-art performance of our method against representative baselines. Further in-depth analysis not only reveals the rationale behind our proposal but also provide insightful interpretations on what the system have learned.

To relieve intensive human-expertise required to design optimization algorithms, recent Meta-Black-Box Optimization (MetaBBO) researches leverage generalization strength of meta-learning to train neural network-based algorithm design policies over a predefined training problem set, which automates the adaptability of the low-level optimizers on unseen problem instances. Currently, a common training problem set choice in existing MetaBBOs is well-known benchmark suites CoCo-BBOB. Although such choice facilitates the MetaBBO's development, problem instances in CoCo-BBOB are more or less limited in diversity, raising the risk of overfitting of MetaBBOs, which might further results in poor generalization. In this paper, we propose an instance generation approach, termed as \textbf{LSRE}, which could generate diverse training problem instances for MetaBBOs to learn more generalizable policies. LSRE first trains an autoencoder which maps high-dimensional problem features into a 2-dimensional latent space. Uniform-grid sampling in this latent space leads to hidden representations of problem instances with sufficient diversity. By leveraging a genetic-programming approach to search function formulas with minimal L2-distance to these hidden representations, LSRE reverse engineers a diversified problem set, termed as \textbf{Diverse-BBO}. We validate the effectiveness of LSRE by training various MetaBBOs on Diverse-BBO and observe their generalization performances on either synthetic or realistic scenarios. Extensive experimental results underscore the superiority of Diverse-BBO to existing training set choices in MetaBBOs. Further ablation studies not only demonstrate the effectiveness of design choices in LSRE, but also reveal interesting insights on instance diversity and MetaBBO's generalization.

The science is still emerging, but I couldn't deny how relaxed I felt. A mallet hovers over a bronze singing bowl, an instrument long used for meditation and relaxation practices. Breakthroughs, discoveries, and DIY tips sent every weekday. I drove up to my first sound bath experience not knowing quite what to expect. The meditative practice, which utilizes chimes, gongs, and an arsenal of "vibrational musical instruments," has existed in various forms for millennia but has seen a post-pandemic resurgence, particularly among the burgeoning, influencer-boosted online wellness community.

High responsiveness and economic efficiency are critical objectives in supply chain transportation, both of which are influenced by strategic decisions on shipping mode. An integrated framework combining an efficient simulator with an intelligent decision-making algorithm can provide an observable, low-risk environment for transportation strategy design. An ideal simulation-decision framework must (1) generalize effectively across various settings, (2) reflect fine-grained transportation dynamics, (3) integrate historical experience with predictive insights, and (4) maintain tight integration between simulation feedback and policy refinement. We propose Sim-to-Dec framework to satisfy these requirements. Specifically, Sim-to-Dec consists of a generative simulation module, which leverages autoregressive modeling to simulate continuous state changes, reducing dependence on handcrafted domain-specific rules and enhancing robustness against data fluctuations; and a history-future dual-aware decision model, refined iteratively through end-to-end optimization with simulator interactions. Extensive experiments conducted on three real-world datasets demonstrate that Sim-to-Dec significantly improves timely delivery rates and profit.

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous optimization problem by characterizing the DAG constraint as a smooth equality one, generally based on polynomials over adjacency matrices. Existing methods place very small coefficients on high-order polynomial terms for stabilization, since they argue that large coefficients on the higher-order terms are harmful due to numeric exploding. On the contrary, we discover that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher-order terms can approximate the DAG constraints much better than the small counterparts. Based on this, we propose a novel DAG learning method with efficient truncated matrix power iteration to approximate geometric series based DAG constraints.

Inspired by Federated Learning, in this paper, we propose personal large models that are distilled from traditional large language models but more adaptive to local users' personal information such as education background and hobbies. We classify the large language models into three levels: the personal level, expert level and traditional level. The personal level models are adaptive to users' personal information. They encrypt the users' input and protect their privacy. The expert level models focus on merging specific knowledge such as finance, IT and art. The traditional models focus on the universal knowledge discovery and upgrading the expert models. In such classifications, the personal models directly interact with the user. For the whole system, the personal models have users' (encrypted) personal information. Moreover, such models must be small enough to be performed on personal computers or mobile devices. Finally, they also have to response in real-time for better user experience and produce high quality results. The proposed personal large models can be applied in a wide range of applications such as language and vision tasks.

Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion process in the gradient domain, where the convergence becomes faster. There are two reasons. First, thanks to the Poisson equation, the gradient domain is mathematically equivalent to the original image domain. Therefore, each diffusion step in the image domain has a unique corresponding gradient domain representation. Second, the gradient domain is much sparser than the image domain. As a result, gradient domain diffusion models converge faster. Several numerical experiments confirm that the gradient domain diffusion models are more efficient than the original diffusion models. The proposed method can be applied in a wide range of applications such as image processing, computer vision and machine learning tasks.

Activation functions are essential components of neural networks. In this paper, we introduce a new activation function called the Truncated and Signed Square Root (TSSR) function. This function is distinctive because it is odd, nonlinear, monotone and differentiable. Its gradient is continuous and always positive. Thanks to these properties, it has the potential to improve the numerical stability of neural networks. Several experiments confirm that the proposed TSSR has better performance than other stat-of-the-art activation functions. The proposed function has significant implications for the development of neural network models and can be applied to a wide range of applications in fields such as computer vision, natural language processing, and speech recognition.