Appendix G

EMA Scoring Algorithm

Mathematical foundation, α parameter selection, and comparison to LRU.

G.1 EMA Update Rule

score_t(p) = α × attention_t(p) + (1 - α) × score_t-1(p)

This creates a "memory" of attention importance that decays gradually.

G.2 Properties

Half-life: t_1/2 = -ln(2) / ln(1-α)
Steady state: For constant attention a, score → a
Decay: Without attention, score → 0 exponentially

G.3 α Selection

α	Half-Life (steps)	Use Case
0.05	13.5	Very stable, long memory
0.1	6.6	Recommended default
0.2	3.1	Faster adaptation

G.4 EMA vs LRU

LRU problem: System prompt at position 5 evicted after 100 steps despite receiving 4% attention every step
EMA solution: Stable 0.04 score keeps it cached

Status: EMA/LRFU-style scoring is a mechanism, not a measured win. In the corrected Revision-2 simulator, policy advantage depends strongly on HBM budget, α, workload, and whether policy metadata survives eviction; see Appendix N.

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