AIRE-Prune: Asymptotic Impulse-Response Energy for State Pruning in State Space Models

Abstract: State space models (SSMs) often sacrifice capacity, search space, or stability to offset the memory and compute costs of large state dimensions. We introduce a structured post-training pruning method for SSMs -- AIRE-Prune (Asymptotic Impulse-Response Energy for State PRUN(E)) -- that reduces each layer's state dimension by directly minimizing long-run output-energy distortion. AIRE-Prune assigns every state a closed-form asymptotic impulse-response energy-based score, i.e., the total impulse-response energy it contributes over an infinite horizon (time), and normalizes these scores layer-wise to enable global cross-layer comparison and selection. This extends modal truncation from single systems to deep stacks and aligns pruning with asymptotic response energy rather than worst-case gain. Across diverse sequence benchmarks, AIRE-Prune reveals substantial redundancy in SISO and MIMO SSMs with average pruning of 60.8%, with average accuracy drop of 0.29% without retraining, while significantly lowering compute. Code: https://github.com/falcon-arrow/AIRE-Prune.