Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time formulations such as the family of Neural Ordinary Differential Equations (Neural ODEs). Generally, they have shown that capturing the underlying dynamics is beneficial for generic tasks like interpolation, extrapolation, and classification. However, existing methods approximate the dynamics using unconstrained neural networks, which struggle to adapt reliably under distributional shifts. In this paper, we recast time-series problems as the continuous ODE-based optimal control problem. Rather than learning dynamics solely from data, we optimize control actions that steer ODE trajectories toward task objectives, bringing control-theoretical performance guarantees. To achieve this goal, we need to (1) design the appropriate control actions and (2) apply effective optimal control algorithms. As the actions should contain rich context information, we propose to employ the discrete-time model to process past sequences and generate actions, leading to a coordinate model to extract long-term temporal features to modulate short-term continuous dynamics. During training, we apply model predictive control to plan multi-step future trajectories, minimize a task-specific cost, and greedily select the optimal current action. We show that, under mild assumptions, this multi-horizon optimization leads to exponential convergence to infinite-horizon solutions, indicating that the coordinate model can gain robust and generalizable performance. Extensive experiments on diverse time-series datasets validate our method's superior generalization and adaptability compared to state-of-the-art baselines.

Invertible neural networks (INNs) have gained attention for solving inverse problems where learning a bijective mapping is essential. However, despite their popularity, little guidance exists on how to select, adapt, or deploy different INN architectures, such as i-ResNet, NICE, or DipDNN, across diverse application domains. In this paper, we provide a unified theoretical and empirical analysis of two major INN families: iterative-contraction networks (e.g., i-ResNet) and triangular coupling networks (e.g., NICE, DipDNN). We show that these models exhibit fundamental tradeoffs in invertibility, expressivity, and compatibility with domain constraints. For example, contractive models fail to recover mappings with large gains or sign flips, whereas triangular schemes inherit rigid channel splits that can restrict feature richness. Building on these insights, we introduce a general-purpose customization framework. It decouples physics-informed constraints from measurement-driven inversion through a parallel INN design. We benchmark representative INNs on cross-domain tasks: edge monitoring, PDE dynamics, and robotic control. Our findings offer first comprehensive design guideline for choosing and adapting INN architectures based on problem structure, shedding light on when and how invertibility-based bidirectional inferences can be reliably applied in practice.

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating dynamics requires extensive calculations and suffers from high truncation errors for the ODE solvers. To address the issue, one intuitive approach is to consider the non-trivial topological space of the data distribution, i.e., a low-dimensional manifold. Existing methods often rely on knowledge of the manifold for projection or implicit transformation, restricting the ODE solutions on the manifold. Nevertheless, such knowledge is usually unknown in realistic scenarios. Therefore, we propose a novel approach to explore the underlying manifold to restrict the ODE process. Specifically, we employ a structure-preserved encoder to process data and find the underlying graph to approximate the manifold. Moreover, we propose novel methods to combine the NODE learning with the manifold, resulting in significant gains in computational speed and accuracy. Our experimental evaluations encompass multiple datasets, where we compare the accuracy, number of function evaluations (NFEs), and convergence speed of our model against existing baselines. Our results demonstrate superior performance, underscoring the effectiveness of our approach in addressing the challenges of high-dimensional datasets.

Learning dynamics is essential for model-based control and Reinforcement Learning in systems operating in changing environments, such as robotics, autonomous vehicles, and power systems. However, limited system measurements, such as those from low-resolution meters, demand sample-efficient learning. Symmetry provides a powerful inductive bias by characterizing equivalent relations in system behavior to improve sample efficiency. While recent methods attempt to discover symmetries from data, they typically assume a single global symmetry group and treat symmetry discovery and dynamic learning as separate tasks, leading to limited expressiveness and error accumulation. In this paper, we propose the Latent Mixture of Symmetries (Latent MoS), an expressive model that captures symmetry-governed latent factors from complex dynamical measurements. Latent MoS focuses on dynamic learning while locally preserving the underlying symmetric transformations. To further capture long-range temporal equivalence, we introduce a hierarchical architecture that stacks Latent MoS blocks across multiple time scales. Numerical experiments across diverse physical systems demonstrate that Latent MoS significantly outperforms state-of-the-art baselines in interpolation and extrapolation tasks while offering interpretable latent representations suitable for future geometric and safety-critical analysis.

Variational quantum algorithms (VQAs) are the leading algorithm for achieving quantum advantage using near-term quantum computers. VQAs use parameterized quantum circuits for inference, and the variational parameters in quantum circuits can be trained using a classical optimizer. The parameters are trained to guide how the quantum bits evolve and make the final measurements closely match the ground truth. However, this way of learning from raw data makes it difficult to capture the underlying dynamic information in the data, especially for time series data. To address this limitation, we proposed continuous variational quantum algorithms (CVQAs) for time series in this paper. CVQAs use quantum variational circuits to parameterize the dynamics of time series, thus they can learn the dynamic information behind the data. After the dynamics are trained, the prediction results will be obtained by a differential equation solver working on the dynamics. Since we aim to model the dynamics of data instead of the data itself, the quantum circuit in our approach will need fewer qubits and variational gates. To evaluate our proposed approach, we compare our model with baseline models on several weather time series. Experimental results prove that our approach has better or equivalent results but with fewer qubits and variational gates compared to baseline models.

Question answering (QA) is a task in the field of natural language processing (NLP) and information retrieval, which has pivotal applications in areas such as online reading comprehension and web search engines. Currently, Bidirectional Encoder Representations from Transformers (BERT) and its biomedical variation (BioBERT) achieve impressive results on the reading comprehension QA datasets and medical-related QA datasets, and so they are widely used for a variety of passage-based QA tasks. However, their performances rapidly deteriorate when encountering passage and context ambiguities. This issue is prevalent and unavoidable in many fields, notably the web-based medical field. In this paper, we introduced a novel approach called the Multiple Synonymous Questions BioBERT (MSQ-BioBERT), which integrates question augmentation, rather than the typical single question used by traditional BioBERT, to elevate BioBERT’s performance on medical QA tasks. In addition, we constructed an ambiguous medical dataset based on the information from Wikipedia web. Experiments with both this web-based constructed medical dataset and open biomedical datasets demonstrate the significant performance gains of the MSQ-BioBERT approach, showcasing a new method for addressing ambiguity in medical QA tasks.