Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation

Abstract:Stage-replay diagnostics reconstruct intermediate token prefixes and treat fresh-prefill continuation as continuation from the decoder state that originally reached the prefix. We audit that assumption at a whole reasoning-stage boundary in a Qwen2.5-derived system. A matched 200-item experiment compares retained live cache with one-shot prefill of identical integer tokens and places an exact replica on both sides. In BF16, replicas remain exact while the constructions differ on 166 suffixes and 20 correctness labels; the accuracy difference is only one point (paired 95% CI [-3.5, +5.5]). A fixed-prefix 2x2 holds all 200 token states constant while crossing construction and precision. The BF16 disagreements recur, whereas FP32 produces no decoded disagreement (95% Wilson upper bound 1.88%). A prospective bridge makes token-by-token incremental and retained live caches bit-exact on 12/12 rows; an all-200 saved-ledger audit reproduces every retained trajectory and comparison fingerprint. Bidirectional transplantation of all 48 key/value layers makes every tested divergent continuation follow its cache donor, both on a selected set at the primary checkpoint (24/24) and an outcome-blind replication at a later checkpoint (43/43). Exact-token replay can therefore be repeatable without preserving live-state fidelity. On the tested states, boundary K/V cache is a causally sufficient carrier of the divergent trajectory, while numerical precision moderates its behavioral expression.

15 pages, 1 figure, 6 tables. Reproducibility artifacts (frozen manifests, token IDs, per-item scores, analysis harnesses) described in Section 3.9

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2607.28495 [cs.LG]

(or arXiv:2607.28495v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.28495 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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