Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

翻译：可识别性是深度隐变量模型可解释性的核心，它确保参数化由数据生成分布唯一确定。然而，对于深度体制转换时间序列模型，其可识别性仍未得到充分探索。本文为多滞后体制转换模型（RSMs）建立了一个通用的理论框架，涵盖马尔可夫转换模型（MSMs）和切换动态系统（SDSs）。对于MSMs，我们将模型表述为时间结构化的有限混合模型，并在非线性高斯设定下证明了体制数量与多滞后转移概率的可识别性。对于SDSs，我们通过时间结构建立了隐变量（在置换与缩放意义下）的可识别性，进而推导出体制依赖的隐因果图（在体制/节点置换意义下）可识别的条件。我们的结果在完全无监督设定下成立，所依赖的架构与噪声假设可通过神经网络设计直接实现。我们补充了一种满足这些假设的灵活变分估计器，并在合成基准测试中验证了理论结果。在神经科学、金融和气候领域的真实数据集上，可识别性带来了更可信的可解释性分析，这对科学发现至关重要。