{"ID":2852055,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.18310","arxiv_id":"2510.18310","title":"Towards Identifiability of Hierarchical Temporal Causal Representation Learning","abstract":"Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hierarchical latent variables from \\textit{single-timestep observed variables}. Interestingly, we find that the joint distribution of hierarchical latent variables can be uniquely determined using three conditionally independent observations. Building on this insight, we propose a Causally Hierarchical Latent Dynamic (CHiLD) identification framework. Our approach first employs temporal contextual observed variables to identify the joint distribution of multi-layer latent variables. Sequentially, we exploit the natural sparsity of the hierarchical structure among latent variables to identify latent variables within each layer. Guided by the theoretical results, we develop a time series generative model grounded in variational inference. This model incorporates a contextual encoder to reconstruct multi-layer latent variables and normalize flow-based hierarchical prior networks to impose the independent noise condition of hierarchical latent dynamics. Empirical evaluations on both synthetic and real-world datasets validate our theoretical claims and demonstrate the effectiveness of CHiLD in modeling hierarchical latent dynamics.","short_abstract":"Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail to capture such dynamics, as they fail to recover the joint distribution of hier...","url_abs":"https://arxiv.org/abs/2510.18310","url_pdf":"https://arxiv.org/pdf/2510.18310v1","authors":"[\"Zijian Li\",\"Minghao Fu\",\"Junxian Huang\",\"Yifan Shen\",\"Ruichu Cai\",\"Yuewen Sun\",\"Guangyi Chen\",\"Kun Zhang\"]","published":"2025-10-21T05:40:17Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}