Inferring Missing Trajectory Data with Temporal Convolutional Networks

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.

Image inpainting aims to recover missing regions while preserving structural consistency. We propose a non-parametric method without network training based on data-guided stochastic dynamics. Starting from a masked image, the missing pixels are evolved through a reverse-time stochastic differential equation with a kernel-weighted correction estimated directly from a reference dataset. This empirical correction guides the reconstruction toward high-density regions of the data distribution without training a neural network or fitting a parametric density model. Experiments on MNIST, Fashion-MNIST, and MVTec show that the proposed method outperforms Mean Fill, Telea, and Navier-Stokes inpainting in PSNR, SSIM, and visual quality. On CelebA, it remains competitive and produces plausible completions for structure-sensitive occlusions. These results demonstrate the effectiveness of empirical reference statistics as a non-parametric prior for image inpainting.

Trajectory representation learning underpins a wide range of trajectory analytics tasks; however, most existing self-supervised approaches, whether discriminative or generative, adopt an open-loop paradigm, relying on fixed data augmentations or random masking without feedback, which limits their ability to generalize and scale. We propose REFINE, a simple yet effective Representation lEarning Framework vIa closed-loop traNscription rEfinement for trajectory data. Drawing upon feedback control theory, REFINE tightly couples road-network-aware generative reconstruction with feedback-driven contrastive learning, enabling the model to capture fine-grained local movement semantics and global spatio-temporal dependencies without manually designed augmentation views. We further provide a control-theoretic analysis that establishes convergence guarantees for the proposed closed-loop optimization. Extensive experiments on four real-world datasets demonstrate that REFINE consistently outperforms state-of-the-art methods across multiple downstream tasks while remaining computationally efficient and scalable. This paper is an extended version of REFINE: Trajectory Representation Learning via Closed-Loop Transcription, to appear in KDD 2026.