numpy

Simulate both phases of ring all-reduce and verify values, preserved inputs and each rank’s payload bytes.

Follow the matrix shapes through a low-rank update. Verify merged inference numerically and show why multiplying sums of adapter factors gives the wrong weights.

Build a small CPU reference, overwrite a bounded KV ring, and compare every step with a recomputed attention window. Keep model semantics separate from eviction.

Derive the scale, handle zero tensors, clamp before casting, and separate rounding error from clipping. Compare one outlier under tensor and channel scales.