DAG-MAMBA: Structure-aware selectivity for directed acyclic graphs State space model

The directed acyclic graph (DAG) induces a partial order, but does not induce a unique node sequence, which causes a structural mismatch between it and the order-sensitive state space model (SSM). Arbitrary topological serialization may make the loop model depend on the relative order of incomparable nodes, even if the order is not part of the graph. We study how to align order-sensitive sequence models with DAGs without committing to an arbitrary linear extension. We propose \method, a sequential robust structural interface, which separates the node-level dependency information from the coarse-grained depth sequence. The local and bounded reachability branches retain the direct relationship and the predecessor-follower relationship, and the nodes with the same longest path depth are pooled into a norm-front token sequence ; we then use Mamba as a learned cross-frontier mixer. The frontier represents that the node index and the selected topology order remain unchanged, but is intentionally designed to be non-injective, so it complements rather than replaces the graph structure. On the code, reference, and neural architecture DAG, complete instantiation is significantly superior to sequential naive Mamba on several tasks and remains competitive with strong graph/DAG baselines. A diagnostic ablation further demonstrated that replacing the learned Mamba transfer with an identical leading-edge mixer on three ablation tasks could match or exceed the complete model. This distinguishes two confusing effects : sequential robustness is provided by the DAG interface, and the marginal value of the learned cross-frontier loop depends on the task. Therefore, we position \method as a Mamba instantiation of a sequential robust DAG interface, rather than as evidence that selective scanning is generally necessary for DAG learning. The simulation code can be obtained in https://github.com/zongjin130/DAG-MAMBA.