Cross-Model KV Cache Transfer in LLM Families: A Closed-Form Linear Mapping for Prefill Reuse

An inference-efficiency method for production stacks that swap between different-sized models in a family (cost-quality cascading, mid-conversation switching, routing) — every swap normally forces the receiver to repay the prefill from scratch. The paper shows cross-model KV caches share substantial linear structure across matched-KV pairs (on Qwen3 14B→32B, one source layer explains 56% of the target's key variance, rising to 79% with several layers), and builds a closed-form per-head ridge mapper: pick the top-k predictive source layers, strip RoPE so the fit is position-free and reusable across context lengths, and fit ridge regression on just 500 calibration sequences.

Across six pairs in three families it retains 73–98% of standalone-prefill accuracy on four pairs (a nonlinear MLP recovers the two failures, +37pp HellaSwag), running 2.7–25× faster than re-prefill and stable across multi-turn handoff. NVIDIA.