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

arXiv: https://arxiv.org/abs/2607.28495 · HTML: https://mlsanity.com/paper/2607.28495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Efficient reasoning and agent inference, one of 12 directions in Efficient LLM inference and serving.
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Placed in

- Efficient LLM inference and serving / [Efficient reasoning and agent inference](https://mlsanity.com/inference/efficient-reasoning-and-agent-inference/)

## Builds on (most cited first, 14 of 14)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Branch-Solve-Merge Improves Large Language Model Evaluation and Generation](https://mlsanity.com/paper/2310.15123/) (2023)
- [Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models](https://mlsanity.com/paper/2509.26626/) (2025)
- [Learning to Reason Across Parallel Samples for LLM Reasoning](https://mlsanity.com/paper/2506.09014/) (2025)
- [PaCoRe: Learning to Scale Test-Time Compute with Parallel Coordinated Reasoning](https://mlsanity.com/paper/2601.05593/) (2026)
- [Deterministic Inference across Tensor Parallel Sizes That Eliminates Training-Inference Mismatch](https://mlsanity.com/paper/2511.17826/) (2025)
- [The Illusion of Equivalence: Systematic FP16 Divergence in KV-Cached Autoregressive Inference](https://mlsanity.com/paper/2604.15409/) (2026)
- [Beyond Consensus: Trace-Level Synthesis in Mixture of Agents](https://mlsanity.com/paper/2605.29116/) (2026)
- [MarginGate: Sparse Margin-Triggered Verification for Batch-Invariant LLM Inference](https://mlsanity.com/paper/2605.30218/) (2026)
- [SPIRAL: Learning to Search and Aggregate](https://mlsanity.com/paper/2606.23595/) (2026)
- [Amortized Reasoning Tree Search: Decoupling Proposal and Decision in Large Language Models](https://mlsanity.com/paper/2602.12846/) (2026)
- [Counterfactual Likelihood Tests for Indirect Influence in Private Reasoning Channels](https://mlsanity.com/paper/2605.19092/) (2026)
- [Re-feeding Is Not Replaying: Measuring Replay Noise in Counterfactual Token-Credit Estimation](https://mlsanity.com/paper/2606.15621/) (2026)

## Built on by (most cited first, 1 of 1)

- [Same Request, Different Answer: Quantization Amplifies Cache-Induced Divergence in LLM Serving](https://mlsanity.com/paper/2609.04748/) (2026)

## Abstract (arXiv)

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.