Longitudinal surveys are a crucial component of behavioral research. Such surveys, however, face significant gaps in the data created by item and unit non-responses as well as semantic gaps resulting from questionnaires, assessed trends, and data collection methods evolving over time. Using 15 waves of vaccination surveys as a test-bed, we demonstrate how modern AI techniques can bridge both item and unit gaps, originating from non-response, and semantic gaps, originating from instrument evolution. We address these gaps through a two-component framework. We leverage LLM-generated semantic embeddings of survey questions to encode question meaning, enabling a Deep & Cross Network used for imputation to jointly model responses across item semantics, individual characteristics, and temporal dynamics. This structure directly addresses survey evolution by operating in learned semantic space. To overcome data scarcity, we use cluster-informed synthetic data generation via hierarchical prompting that produces synthetic responses preserving distributional properties and empirical cluster structure. Our approach achieves a strong improvement in semantic gap tasks and 80-90% synthetic data fidelity, providing practical solutions for evolving longitudinal studies.

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep neural networks (e.g., RNN, LSTM) because of the exploding gradient issue. Gradient clipping is usually employed to address this issue in the single machine setting, but exploring this technique in the distributed setting is still in its infancy: it remains mysterious whether the gradient clipping scheme can take advantage of multiple machines to enjoy parallel speedup. The main technical difficulty lies in dealing with nonconvex loss function, non-Lipschitz continuous gradient, and skipping communication rounds simultaneously. In this paper, we explore a relaxed-smoothness assumption of the loss landscape which LSTM was shown to satisfy in previous works, and design a communication-efficient gradient clipping algorithm. This algorithm can be run on multiple machines, where each machine employs a gradient clipping scheme and communicate with other machines after multiple steps of gradient-based updates. Our algorithm is proved to have $O\left(\frac{1}{N\epsilon^4}\right)$ iteration complexity and $O(\frac{1}{\epsilon^3})$ communication complexity for finding an $\epsilon$-stationary point in the homogeneous data setting, where $N$ is the number of machines. This indicates that our algorithm enjoys linear speedup and reduced communication rounds. Our proof relies on novel analysis techniques of estimating truncated random variables, which we believe are of independent interest. Our experiments on several benchmark datasets and various scenarios demonstrate that our algorithm indeed exhibits fast convergence speed in practice and thus validates our theory.