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

KV caching is a ubiquitous optimization in autoregressive transformer inference, long presumed to be numerically equivalent to cache-free computation. This assumption fails under standard FP16 precision: cache-ON and cache-OFF execution paths employ different floating-point accumulation orderings which, due to FP16 non-associativity, produce a deterministic divergence in decoded token sequences. Across three open-weight models (LLaMA-2-7B, Mistral-7B-v0.3, Gemma-2-2B) evaluated on GSM8K, we observe a 100% token divergence rate across all sampling strategies, including greedy decoding, which rules out sampling randomness as a cause, and also with cache-ON yielding higher accuracy in 8 of 9 conditions, where the accuracy difference serves as an indicator that the divergence direction is systematic rather than random. Controlled FP32 falsification reduces divergence by eight orders of magnitude, eliminates token flips, and drops the flip rate to exactly 0.0%, confirming FP16 non-associativity as the sole causal driver. Layer-wise drift profiling reveals architecturally predictable propagation patterns: models using Grouped-Query Attention exhibit sharp divergence at the first layer, while Gemma's larger head dimension and sliding window attention produce uniform accumulation across all layers. Finally, activation patching of the entire residual stream fails to recover the cache-free trajectory, localizing the causal variable to the stateful KV cache. These findings establish that FP16 KV cache inference is fundamentally non-equivalent to recomputation and provide a mechanistic framework for understanding numerical instability in modern LLM inference systems.

Prefill-decode (PD) disaggregation decouples prompt processing from token generation, but it also turns the key-value (KV) cache into a network payload. Existing PD-side KV reduction methods are mostly binary: selected tokens are transmitted at full precision and the rest are not transmitted. This paper argues that binary selection leaves a useful design space unused. SpectrumKV assigns a precision level to each token instead: attention sinks and other high-importance tokens are protected at FP16, medium-importance tokens are sent at INT8, and low-importance tokens are sent at INT4 when the model can tolerate it. The main practical complication is that INT4 tolerance is model-dependent. Qwen2.5-7B catastrophically fails under INT4 KV quantization, while Mistral-7B and Gemma-2-9B remain stable. SpectrumKV therefore runs a lightweight deployment-time probe: three aggressive NIAH trials under a 3-tier policy. Models that pass use FP16+INT8+INT4; models that fail fall back to FP16+INT8. Across Qwen2.5-7B-Instruct, Mistral-7B-Instruct-v0.3, and Gemma-2-9B-it, SpectrumKV improves quality at the same transfer budget. At a 50% normalized KV budget on WikiText-2, SpectrumKV changes perplexity by +1.97%,-0.06%, and-0.44%, respectively, compared with PDTrim's +25.85%, +22.07%, and +35.63%. On NIAH retrieval at 4096 tokens, the adaptive policy reaches 52.6% on Qwen at the aggressive b=0.3 budget versus 26.3% for PDTrim, and reaches 100% by b=0.5; Mistral and Gemma preserve retrieval under the 3-tier policy. End-to-end GPU timing of the transfer path shows 50-62% TTFT reductions at b=0.5. These results suggest that PD KV transfer should be treated as a precision-allocation problem, not only as token pruning.

Per-token counterfactual credit estimation asks which token in a language-model rollout caused the final answer to be right or wrong: cut the transcript at a pivot, substitute an alternative token, replay continuations, and compare outcomes. Published methods re-feed the transcript prefix as a fresh prompt, assuming this reproduces the state the model passed through during generation. We measure what that assumption costs on a stock inference engine, with a three-pass design: continuations resumed from the verified decode-time KV state, an identical second exact pass (a replica noise floor), and a re-feed pass. Across six configurations and three models (including a GRPO-trained checkpoint), at low-margin decision tokens, re-feeding changes the credit estimate at rates 14-28 percentage points above the replica floor (7-21pp under a treatment-independent conditioning; problem-clustered t = 2.9-6.4). Most changes are zero-boundary crossings of the quantized estimator rather than polarity reversals, and the perturbation is consistent with mean-zero, so averaged quantities are largely safe; but selection is not: a critical-token set chosen by thresholding $|\hat{A}_t|$ under re-feed overlaps the exact-resume selection at Jaccard 0.34-0.90, versus a 0.63-0.96 replica ceiling. A causal confirmation closes the loop: under vLLM's batch-invariant kernels all three passes are identical on every measured channel, with both disagreement rates exactly zero. Replica passes themselves disagree on 9-23% of eligible estimates: single-sample credit measurements at decision tokens are unreliable under any replay. Settings were fixed in advance; exact-pass cache hits in the second campaign are instrumented (100% hit rate, 3,434 pivots); total compute was under 10 USD. We recommend that counterfactual credit studies resume decoder state or use batch-invariant kernels, and report a replica floor.