Constrained latent state modeling: A unifying perspective on representation learning under competing constraints

Learning latent representations from temporal, multimodal, and partially observed data requires specifying what information a latent state should retain, discard, and organize. Existing approaches encode these requirements through heterogeneous objectives, making methods difficult to compare and learned representations difficult to interpret. We propose Constrained Latent State Modeling (CLSM), a conceptual framework that characterizes latent states through six complementary properties: predictive sufficiency, minimality, temporal coherence, observation compatibility, invariance to nuisance factors, and structural constraints. CLSM separates these properties from the surrogate objectives used to induce them and from the diagnostics used to evaluate them, and clarifies how combinations of constraints can improve identifiability by restricting the space of admissible representations. We reinterpret major representation-learning families through this common design space and illustrate the framework with a controlled synthetic benchmark. The experiments show how objectives produce distinct latent organizations and empirical trade-offs depending on the prediction target, surrogate formulation, parameterization, and optimization. Companion repository containing the reference implementation, reproducible experiments, documentation, and model cards: https://github.com/gwenole-quellec/clsm