Module quat_scan 

Memory-efficient quaternion cumulative-product scan (custom backward)

The Quaternion4D forward composes its per-step rotations with a cumulative product over the sequence (crate::mamba3::rotation::quat_cumprod, a Hillis–Steele parallel scan). Expressed in plain autodiff that scan retains O(log seq) full-sequence intermediates for the backward pass — fast, but memory-hungry.

This module provides the recompute alternative, mirroring the SSD SerialRecalculated design: a Mamba3QuatScanBackendExt trait whose Autodiff impl (backward) registers a single custom Backward node that saves only the leaf inputs (the per-step quaternions and the carry) and recomputes the scan during backprop. The gradient is the exact quaternion VJP of the cumulative product, evaluated with parallel ops (a prefix product + a reverse-cumsum) — no token loop, so the saved memory does not buy back a slow backward.

quat_cumprod_recalculated is the high-level drop-in for quat_cumprod used by the Quaternion4D forward path; the plain-autodiff quat_cumprod stays as the verified reference (the tests assert the two agree on values and gradients).

Re-exports

pub use quat_scan::Mamba3QuatScanBackendExt;

pub use quat_scan::quat_cumprod_recalculated;

Modules

backward

The registered custom Backward node (autodiff op) + the recompute gradient math.

quat_scan

The backend-extension trait, its primitive default body, the per-backend impls, and the quat_cumprod_recalculated high-level wrapper.