An Exact Instrument for State Usage in Selective State-Space Models, and the Input-Driven Migration It Reveals
Selective state-space models such as Mamba route information through a bank of first-order modes whose input coupling is set by a learned selection mechanism. We give an exact instrument for measuring how a trained model uses these modes. Because the state matrix is diagonal, each channel's output decomposes exactly into per-mode contributions, and a per-(layer, channel, window) Gram tensor yields the exact output error of dropping any subset of modes, offline, at any budget. Validated against the reference implementation to a relative error of $2.3\times10^{-7}$ on the Mamba-1 family where it is exact, the instrument predicts a layer's deployed pruning error to a median relative deviatio...
| Authors | Raktim Bhattacharya |
|---|---|
| Primary category | cs.LG |
| Published | 13 July 2026 |
| Last updated at source | 11 August 2026 |
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