PCDM: Shared Structure and Local Modulation for Dynamic Causal Discovery

Two common approaches to dynamic causal discovery model nonstationarity as smooth temporal variation or latent regime switching. One absorbs changes in mechanisms into smooth drift, blurring abrupt regime shifts into gradual variation when regimes are short. Another introduces latent states with regime-specific edges and mechanisms, allowing ordinary fluctuations to harden into pseudo-mechanisms exactly where evidence is weakest. We therefore propose the Piecewise Causal Dynamic Model (PCDM). PCDM couples state-specific effective graphs through shared candidate scores and sparse local gates. Finite-sample analysis of a restricted regression analogue characterizes conditions for sharing benefits. Shared scores alone do not ensure that local gates select useful parents. We introduce observation-informed gate restart (INFO): a posterior-weighted additive fit ranks candidate inputs, and the resulting order reassigns existing gate strengths before neural learning resumes. On calibrated additive and core–private interaction mechanisms, INFO improves state-specific edge localization and lowers finite-response error relative to matched continuation and random-reassignment controls. Matched screening controls support the value of observation-specific state information for parent selection on additive mechanisms. Additional structured-state diagnostics show that state-inference bottlenecks can be substantially reduced, while the added benefit of sharing for private-edge localization remains to be established.