On the Identification of Temporally Causal Representation with Instantaneous Dependence
Existing time-series causal representation learning methods typically neglect instantaneous causal relationships, while emerging approaches accommodating such dependencies rely on latent-variable interventions or grouped observational data—conditions rarely satisfied in practice. To address this, we propose IDOL, the first framework enabling unique identification of latent causal processes with instantaneous dependencies without requiring interventions or data grouping. Theoretically, IDOL introduces sparse influence constraints—unifying delayed and instantaneous causal modeling—and temporal context variability, establishing strong identifiability guarantees. Methodologically, it integrates temporal variational inference with gradient-driven sparse regularization to jointly estimate latent variables and the causal graph. Experiments demonstrate that IDOL achieves exact structural recovery on synthetic benchmarks and significantly improves long-horizon prediction accuracy and causal interpretability across multiple human motion forecasting datasets.