Learning-enabled controllers with stability certificate functions have demonstrated impressive empirical performance in addressing control problems in recent years. Nevertheless, directly deploying the neural controllers onto actual digital platforms requires impractically excessive communication resources due to a continuously updating demand from the closed-loop feedback controller. We introduce a framework aimed at learning the event-triggered controller (ETC) with optimal scheduling, i.e., minimal triggering times, to address this challenge in resource-constrained scenarios. Our proposed framework, denoted by Neural ETC, includes two practical algorithms: the path integral algorithm based on directly simulating the event-triggered dynamics, and the Monte Carlo algorithm derived from new theoretical results regarding lower bound of inter-event time. Furthermore, we propose a projection operation with an analytical expression that ensures theoretical stability and schedule optimality for Neural ETC. Compared to the conventional neural controllers, our empirical results show that the Neural ETC significantly reduces the required communication resources while enhancing the control performance in constrained communication resources scenarios.

Aspect-Based Sentiment Analysis (ABSA) stands as a crucial task in predicting the sentiment polarity associated with identified aspects within text. However, a notable challenge in ABSA lies in precisely determining the aspects’ boundaries (start and end indices), especially for long ones, due to users’ colloquial expressions. We propose DiffusionABSA, a novel diffusion model tailored for ABSA, which extracts the aspects progressively step by step. Particularly, DiffusionABSA gradually adds noise to the aspect terms in the training process, subsequently learning a denoising process that progressively restores these terms in a reverse manner. To estimate the boundaries, we design a denoising neural network enhanced by a syntax-aware temporal attention mechanism to chronologically capture the interplay between aspects and surrounding text. Empirical evaluations conducted on eight benchmark datasets underscore the compelling advantages offered by DiffusionABSA when compared against robust baseline models. Our code is publicly available at https://github.com/Qlb6x/DiffusionABSA.

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated spatial gradients as additional inputs to a neural network. Furthermore, we utilize the estimated temporal gradient as the optimization objective for the output of the neural network. Later, the trained neural network generates more data points through an ODE solver without participating in the computational graph, facilitating more accurate estimations of gradients based on Fourier analysis. These two steps form a positive feedback loop, enabling accurate dynamics modeling in our framework. Consequently, our approach outperforms state-of-the-art methods in terms of training time, dynamics prediction, and robustness. Finally, we demonstrate the superior performance of our framework using a number of representative complex systems.

In order to stabilize nonlinear systems modeled by stochastic differential equations, we design a Fast Exponentially Stable and Safe Neural Controller (FESSNC) for fast learning controllers. Our framework is parameterized by neural networks, and realizing both rigorous exponential stability and safety guarantees. Concretely, we design heuristic methods to learn the exponentially stable and the safe controllers, respectively, in light of the classical theory of stochastic exponential stability and our established theorem on guaranteeing the almost-sure safety for stochastic dynamics. More significantly, to rigorously ensure the stability and the safety guarantees for the learned controllers, we develop a projection operator, projecting to the space of exponentially-stable and safe controllers. To reduce the highly computational cost for solving the projection operation, approximate projection operators are delicately proposed with closed forms that map the learned controllers to the target controller space. Furthermore, we employ Hutchinson's trace estimator for a scalable unbiased estimate of the Hessian matrix that is used in the projection operator, which thus allows for reducing computational cost and, therefore, can accelerate the training and testing processes. More importantly, our approximate projection operations are applicable to the nonparametric control methods, improving their stability and safety performance. We empirically demonstrate the superiority of the FESSNC over the existing methods.

Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another through the simulation-free learning of the neural ordinary differential equations (ODEs). During inference, however, the learned model often requires multiple neural network evaluations to accurately integrate the flow, resulting in a slow sampling speed. We attribute the reason to the inherent (joint) heterogeneity of source and/or target distributions, namely the singularity problem, which poses challenges for training the neural ODEs effectively. To address this issue, we propose a more general framework, termed Switched FM (SFM), that eliminates singularities via switching ODEs, as opposed to using a uniform ODE in FM. Importantly, we theoretically show that FM cannot transport between two simple distributions due to the existence and uniqueness of initial value problems of ODEs, while these limitations can be well tackled by SFM. From an orthogonal perspective, our framework can seamlessly integrate with the existing advanced techniques, such as minibatch optimal transport, to further enhance the straightness of the flow, yielding a more efficient sampling process with reduced costs. We demonstrate the effectiveness of the newly proposed SFM through several numerical examples.

Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection between deep neural networks and dynamical systems. In this article, we introduce a new sort of continuous-depth neural network, called the Neural Piecewise-Constant Delay Differential Equations (PCDDEs). Here, unlike the recently proposed framework of the Neural Delay Differential Equations (DDEs), we transform the single delay into the piecewise-constant delay(s). The Neural PCDDEs with such a transformation, on one hand, inherit the strength of universal approximating capability in Neural DDEs. On the other hand, the Neural PCDDEs, leveraging the contributions of the information from the multiple previous time steps, further promote the modeling capability without augmenting the network dimension. With such a promotion, we show that the Neural PCDDEs do outperform the several existing continuous-depth neural frameworks on the one-dimensional piecewise-constant delay population dynamics and real-world datasets, including MNIST, CIFAR10, and SVHN.

Control problems are always challenging since they arise from the real-world systems where stochasticity and randomness are of ubiquitous presence. This naturally and urgently calls for developing efficient neural control policies for stabilizing not only the deterministic equations but the stochastic systems as well. Here, in order to meet this paramount call, we propose two types of controllers, viz., the exponential stabilizer (ES) based on the stochastic Lyapunov theory and the asymptotic stabilizer (AS) based on the stochastic asymptotic stability theory. The ES can render the controlled systems exponentially convergent but it requires a long computational time; conversely, the AS makes the training much faster but it can only assure the asymptotic (not the exponential) attractiveness of the control targets. These two stochastic controllers thus are complementary in applications. We also investigate rigorously the linear control in both convergence time and energy cost and numerically compare it with the proposed controllers in these terms. More significantly, we use several representative physical systems to illustrate the usefulness of the proposed controllers in stabilization of dynamical systems.