time embedding interpolation

This work addresses the challenge of modeling irregularly and asynchronously observed time series data by proposing a continuous-time embedding method that operates without interpolation or imputation. The approach directly encodes observations as increments and constructs a continuous, injective embedding via the log-signature over intervals, enabling online computation while avoiding full path reconstruction. Built upon the Log-NCDE framework and the concept of rectangular control paths, the proposed embedding preserves the structural fidelity of the original data and maintains universality over compact subsets of the input space. Empirical evaluations demonstrate that the method achieves high accuracy, computational efficiency, and strong robustness to sparsity and asynchronicity across both synthetic dynamical systems and real-world temporal datasets.

This work addresses probabilistic inference—forecasting, abduction, and intermediate-state estimation—for high-dimensional time series. We propose a probabilistic representation framework grounded in temporal contrastive learning. We provide the first theoretical proof that the learned latent states follow a Gaussian Markov chain structure, thereby reducing complex probabilistic inference to closed-form algebraic operations in a low-dimensional space: matrix inversion for abduction and linear interpolation for intermediate-state estimation. Integrating temporal contrastive learning, Gaussian graphical models, and linear-algebraic inference, our approach enables analytically tractable, efficient, and interpretable probabilistic reasoning. Empirical validation on synthetic tasks with up to 46 dimensions confirms the validity and scalability of the closed-form solutions, achieving substantial reductions in computational complexity compared to conventional sampling- or optimization-based methods.

This work investigates the theoretical underpinnings of memorization and overfitting in stochastic interpolation generative models. Focusing on continuous-time stochastic differential equations and their Euler discretization, it provides the first rigorous theoretical definitions of overfitting and underfitting in generative modeling and derives closed-form expressions for the optimal velocity field and score function. The analysis reveals that generated samples can be expressed as training samples perturbed by three controllable error terms, whose bias is jointly determined by the discretization step size and estimation error. Synthetic experiments corroborate the theoretical prediction that generated samples cluster around the training data distribution, highlighting the critical roles of error accumulation and noise modeling in the model’s reconstruction capability.

4D medical image interpolation faces a fundamental trade-off between temporal resolution and reconstruction fidelity. To address this, we propose the first continuous spatiotemporal motion modeling framework inspired by fluid dynamics principles, jointly leveraging Eulerian and Lagrangian descriptions. Our method employs implicit neural representations to ensure both spatial and temporal continuity, enabling training-free, patient-specific optimization. Crucially, it abandons conventional discrete deformation fields in favor of parameter-free forward deformation modeling, thereby substantially improving motion representation accuracy and generalizability. Evaluated on multi-center 4D CT and MRI datasets, our approach achieves average improvements of +3.2 dB in PSNR and +0.04 in SSIM over prior state-of-the-art methods, while operating at 2.1× faster inference speed. Moreover, it requires no large-scale annotated data, making it highly practical for clinical deployment.

This paper addresses the challenge of dynamically modeling time-varying vector sets—such as spatiotemporal crime distributions or evolving word embeddings. We propose a distribution-level temporal modeling framework based on infinite-dimensional Gaussian processes (GPs). Unlike conventional point-wise approaches, our method treats each time-point’s vector set as a probability distribution and employs kernel embedding with random Fourier features to achieve scalable, low-dimensional temporal representations. To our knowledge, this is the first work extending GPs to model distributions over vector sets, enabling interpretable, structure-aware tracking and visualization of cross-temporal distributional shifts. Evaluated on crime hotspot migration and semantic evolution tasks, our approach significantly improves robustness and interpretability in detecting dynamic patterns. The framework establishes a novel paradigm for time-series analysis of distributional data.

This paper addresses the problem of inferring latent continuous-time dynamical trajectories from sparse, discrete-time observational snapshots—particularly in settings lacking ground-truth path annotations, such as single-cell developmental trajectory inference. To this end, we propose ALI-CFM, a novel method that employs adversarial learning to optimize a neural parameterization of interpolation curves, jointly learning both the underlying dynamic vector field and smooth trajectories within a multi-marginal flow matching framework. We provide theoretical guarantees showing that, under mild conditions, ALI-CFM uniquely recovers the true continuous evolution path. Crucially, it requires no trajectory-level supervision and explicitly enforces distributional consistency across all observed time points. Empirically, ALI-CFM achieves state-of-the-art performance on single-cell trajectory prediction tasks and significantly outperforms existing baselines on spatial transcriptomics and cell tracking benchmarks.

This work addresses the challenge of modeling irregular multivariate time series with asynchronous observations and non-uniform sampling. Existing approaches either lose continuous-time semantics through discretization or incur high computational costs via ordinary differential equation solvers. To overcome these limitations, the authors propose WrapFlow, a novel framework that introduces continuous-time tokenization and a gap-aware mechanism to directly encode raw events while explicitly modeling unobserved intervals. WrapFlow leverages a standard Transformer to capture long-range dependencies and employs a residual flow matching training paradigm that avoids numerical simulation, enabling efficient continuous-time prediction. Evaluated on multiple real-world datasets, WrapFlow achieves state-of-the-art performance, generating high-quality continuous forecasts with only a small fixed number of rollback steps.

Existing time series generative models suffer from limited expressivity and poor adaptability to irregularly sampled observation grids. This work proposes G-SLiCEs, a continuous-time generative model based on Structured Linear Controlled differential equations (SLiCEs), which achieves high expressivity through continuous flow matching in path space. We establish, for the first time, that SLiCEs can approximate any continuous causal pushforward path law under the Wasserstein-∞ metric, thereby enabling universal time series generation and introducing maximal expressivity into continuous-time generative modeling. The method natively supports arbitrary observation time grids and significantly outperforms existing approaches in irregularly sampled settings, demonstrating superior performance in probabilistic forecasting and downstream tasks.