CAST: Structural Inductive Biases for Zero-Inflated Sequence Learning

Zero-inflated sequences pose a distinctive learning challenge: exact zeros may encode inactivity rather than ordinary low-magnitude observations, yet many sequence models process both on the same numerical scale. We introduce CAST, a structural learning framework that separates observed activity from active-state magnitude and uses the resulting temporal organization as an inductive bias for sparse sequence prediction. CAST first learns a temporally ordered graph through a hurdle-style two-part structural model; under the stated structural assumptions this graph admits a causal interpretation, while otherwise it represents directed temporal dependence. The learned graph is then embedded in hyperbolic space to obtain hierarchy-aware positional representations, which are transformed into sample-adaptive gates that modulate nonlinear basis functions in a Kolmogorov-Arnold Network. Our analysis characterizes the population target of the two-part likelihood, the score shift induced by fitting inactive zeros with a continuous objective, and complementary guarantees for hyperbolic representation, radial ordering, realized gate energy, and gate-conditioned sensitivity. Controlled synthetic studies isolate these mechanisms, while real-world benchmarks demonstrate consistent predictive gains over competitive statistical and deep sequence baselines.