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An Exact Instrument for State Usage in Selective State-Space Models, and the Input-Driven Migration It Reveals

paperactiveprovisionalan-exact-instrument-for-state-usage-in-selective-state-space-models-and-the-input-driven-migration-it-reveals-eba45e86·1 events·first seen Jul 14, 2026

Aliases: An Exact Instrument for State Usage in Selective State-Space Models, and the Input-Driven Migration It Reveals

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Mamba Falcon Mamba

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Recent events (1)

5arXiv · cs.LG·Jul 14, 2026·source ↗

Exact instrument for state-mode usage in Mamba SSMs reveals input-driven state migration

A new arXiv paper introduces an exact analytical instrument for measuring how selective state-space models (Mamba-1, Mamba-2, Falcon-Mamba) allocate their state modes across inputs, using a per-(layer, channel, window) Gram tensor that predicts pruning error to near-machine-precision. The key empirical finding is that trained models dynamically reallocate which modes carry signal depending on the input context, and that this migration is driven primarily by the input-dependent write map B_t rather than the timestep parameter typically associated with selectivity. Input-scheduled mode pruning based on this instrument outperforms static and Hankel-based rankings at all scales tested (130M–7B), matching unpruned model quality at half the state budget in offline evaluation.

Evaluation and Benchmarking Inference Economics Mamba An Exact Instrument for State Usage in Selective State-Space Models, and the Input-Driven Migration It Reveals Falcon Mamba