Module serial 

Serial-over-chunks SSD with plain autodiff backward.

Serial-over-chunks SSD (Mamba-3 double-SSD pathway)

The MIMO-first chunkwise scan as a serial loop over chunks, structured like the five Mamba-2 kernels (super::super) but generalised over the mimo_rank axis: the chunk and rank axes are fused into a single length L·M for the intra-chunk products. The standard kernels here are reused by both the γ-pass and the β-pass of the double-SSD decomposition (the caller pre-scales v by γ or β and shifts the β inputs).

• K1 k1_ssd_chunk_cumsum — per-chunk cumulative Δ·A decays.
• K2 k2_ssd_bmm — the intra-chunk C·Bᵀ block matmul (fused L·M).
• K3 k3_ssd_chunk_state — each chunk’s end-state contribution.
• K4 k4_ssd_state_passing — the serial inter-chunk scan.
• K5 k5_ssd_chunk_scan — combines intra- and inter-chunk parts into y.

Produces identical values/gradients to super::minimal; SISO (mimo_rank = 1) is the special case where the fused length equals the chunk length. Gradients flow through plain autodiff.

Functions

k1_ssd_chunk_cumsum

Compute the intra-chunk cumulative log-decay and per-chunk decay totals.

k2_ssd_bmm

Compute the intra-chunk CB matrix on fused (mimo_rank-into-chunk_len) tensors.

k3_ssd_chunk_state

Compute the SSM state at the end of each chunk, assuming zero initial hidden state.

k4_ssd_state_passing

Propagate hidden state across chunk boundaries using a sequential scan.

k5_ssd_chunk_scan

Compute the chunk output by combining the intra-chunk (diagonal) and inter-chunk (off-diagonal) contributions.