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.

Production deployments often swap between different-sized models in a family for cost-quality cascading, mid-conversation switching, and routing, and each swap forces the receiver to repay the prefill from scratch. We propose cross-model KV cache transfer, where the receiver reuses the source's KV cache, skipping prefill. We find that cross-model KV has substantial linear structure across matched-KV pairs, where source and target share KV head count and per-head dimension. On Qwen3 14B->32B, one source layer explains 56% of variance in the target's keys and 32% in values, rising to 79% and 65% with multiple source layers. Building on this, we design a closed-form ridge mapper that operates per head and proceeds in three steps. First, for each target layer we select the top-k most predictive source layers and concatenate their KV as input. Second, we strip RoPE from the keys before mapping, so the fit is position-free and reusable across context lengths. Third, we fit ridge regression on a small calibration set of 500 FineWeb-Edu sequences of 1,024 tokens each. Surprisingly, across six pairs in three families, this linear mapper retains 73-98% of the receiver's standalone-prefill accuracy on four pairs, while two degrade sharply. A nonlinear MLP recovers up to +37 pp HellaSwag retention on the failures. The mapper runs 2.7-25x faster than re-prefill and remains stable across multi-turn handoff, making cross-model KV cache transfer practical.