Beyond Mean Attention: Diversity-Aware, Layer-Wise Scoring for KV Cache Eviction
KV cache eviction methods such as SnapKV and PyramidKV rank tokens solely by mean attention over a small observation window. We study a unified score, $μ_i+λ_1σ_i+λ_2\mathrm{corr}(i,S)$, adding attention dispersion across window queries and redundancy relative to selected tokens. For $λ_2<0$, the score penalizes similarity to selected tokens as in maximal marginal relevance (MMR), without extra forward passes. To test whether this relevance-diversity balance should vary with depth, we compare fixed global coefficients with three-segment and quadratic profiles. Only these depth profiles are searched on a development split under a $\sinh$ reparameterization. On all 16 English LongBench datasets with Mistral-7B at a budget of 64 entries per layer, a single global diversification constant improves 13 of 16 datasets (macro +1.1); the gain holds at budget 32 and narrows at 128. Per-dataset search finds no detectable layer structure on most datasets; on passage retrieval it finds a large one: a mid-layer sign flip that rewards similarity and is worth +9.6 over the baseline at budget 64 and, without re-tuning, +13.2 over the global constant at budget 128. Ablations attribute the gain to the redundancy term; replaying every accepted search state on the held-out test set separates genuine structure from tuning noise.