Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation
arXiv:2607.28495
The paper investigates how the key/value cache in transformer language models affects token generation, showing that cache contents alone can reproduce divergent outputs and that numerical precision (BF16 vs FP32) influences the consistency of these reproductions.
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