Neural Belief-State Filtering with Cross-Variable Coupling for Irregular Time Series

While many sequence models assume evenly spaced observations, in domains such as intensive care different measurements and interventions occur at irregular, asynchronous times, and the underlying state is only partially observed. We introduce Neural Belief-State Filtering (NBSF), a continuous-discrete filter that maintains a probabilistic belief over observed and latent variables, propagates it across irregular gaps with a structured exponential-decay backbone and a gap-dependent nonlinear residual, and assimilates each observation through a learned, innovation-driven update. The distinguishing feature of NBSF is that an observation of one variable can directly revise the belief about other, currently unobserved variables at event time rather than only influencing them later through temporal propagation and it does so without maintaining a dense filtering covariance. We study three assimilation variants: a local-coordinate control that updates only the observed variable, a learned dense cross-variable gain, and a nonlinear cross-variable update. Across four clinical benchmarks and a controlled sensing task, event-time cross-variable assimilation is most useful when direct target observations are scarce, and its advantage grows under target suppression; the dense-gain variant provides the most consistent benefit, while the nonlinear update shows dataset-dependent gains. Parameter-matched ablations show these gains are not explained by model size. Our central finding is that event-time cross-variable information flow is the more consistent mechanism under target scarcity, whereas additional nonlinear update complexity is not consistently beneficial. NBSF uses only $\sim$140K–170K parameters, provides an explicit probabilistic predictive belief whose calibration is evaluated in-distribution, and achieves competitive performance across established clinical irregular-time-series benchmarks.