Identifiable Signed Causal Learning via Latent Stochastic Differential Equations for Inferring Brain Dynamic Effective Connectivity

Abstract

Understanding how brain regions interact to support cognitive tasks requires characterizing directed causal influences among them, known as effective connectivity (EC). As inter-regional coupling changes over time, a dynamic EC (dEC) estimate is required to track this temporal variation. Existing dEC learning methods typically lack a causal rationality guarantee or an identifiability analysis, and output unsigned connectivity that cannot distinguish excitatory from inhibitory influences, which limits further study of brain mechanisms. We propose ISCL, a latent stochastic differential equation framework that derives dEC from latent dynamics through a causal influence operator defined in observation space. As established by a rationality theorem, the operator captures a directed interventional response at each brain state, and under invariance assumptions the operator is identifiable from data, with its signed output separating excitatory from inhibitory influences. On synthetic benchmarks, \model recovers the causal structure on Lorenz96 and achieves the lowest mean structural Hamming distance among compared methods on NetSim, while preserving signed influence structures that distinguish excitatory from inhibitory interactions. Applied to HCP Social Cognition task-fMRI, ISCL reveals a signed architecture whose stability across seeds supports the identifiability guarantee, identifies dominant source and target networks consistent with social-cognition systems, and shows that condition-specific training strengthens causal outflow from the default-mode and frontoparietal networks during theory-of-mind processing. In this task, the recovered signed structure reveals network-level excitatory and inhibitory organization, with the dorsal-attention network as the only consistently positive out-strength source.