Figure: a line chart of cache hit rate in per cent against the EMA decay constant alpha on a logarithmic x-axis decreasing to the right, at a 32 gibibyte HBM budget, experiment e2 with one seed. The seven plotted values are alpha 0.5 at 37.20 per cent, alpha 0.3 at 38.84, alpha 0.15 at 44.33, alpha 0.05 at 55.96, alpha 0.01 at 31.54, alpha 0.003 at 25.47 and alpha 0.001 at 24.44. Two horizontal reference lines mark LRU at 36.85 per cent, drawn long-dashed, and LFU at 15.56 per cent, drawn dotted. The curve has an interior optimum at alpha approximately 0.05, worth plus 19.1 points over LRU, and then falls away as alpha approaches zero, ending at 24.44 which is below LRU and still well above LFU. There is no convergence onto LFU as alpha approaches zero; the Revision 1 claim of monotonic convergence is withdrawn. Simulated and provisional: a single data-structure defect in Revision 1 inverted four of five findings.

Figure 11.1 · Simulated (provisional)

Hit rate against α at 32 GiB — an interior optimum, and no convergence onto LFU

Experiment e2, one seed, 32 GiB HBM budget over a 512 GiB tier. Read this grid against its own baselines only; the e1 sweep in the budget table is a different experiment with different reference values.

Standing caveat — simulated, provisional, not settled. A single data-structure defect in Revision 1 of this simulator inverted four of five findings (99.6% wrong victims for EMA α=0.15). Revision 2 is the corrected rebuild: no Belady bound, no bandwidth/queueing model, whole-context residency assumed, synthetic workload, 2–3 seeds, no hardware validation. CANONICAL-NUMBERS.md §3.
0102030405060hit rate (%)0.50.30.150.050.010.0030.001EMA decay constant α — log scale, decreasing to the rightLRU 36.85LFU 15.56α = 0.5 · 37.20%37.20α = 0.3 · 38.84%38.84α = 0.15 · 44.33%44.33α = 0.05 · 55.96%α = 0.01 · 31.54%31.54α = 0.003 · 25.47%25.47α = 0.001 · 24.44%24.44α = 0.05 · 55.96 — interior optimum+19.1 points over LRUno convergence onto LFUas α → 0 the curve falls away from the optimum
EMA hit rate at 32 GiB, experiment e2 (1 seed)LRU 36.85 — long-dash reference lineLFU 15.56 — dotted reference line
Table view
PolicyHit rate (%)
EMA α = 0.537.20
EMA α = 0.338.84
EMA α = 0.1544.33
EMA α = 0.0555.96
EMA α = 0.0131.54
EMA α = 0.00325.47
EMA α = 0.00124.44
LRU36.85
LFU15.56

The shape is the point, not the peak.Hit rate rises from α = 0.5 to an interior optimum at α ≈ 0.05 (55.96%, +19.1 points over LRU), then falls away through 0.01, 0.003 and 0.001, ending below LRU. A decayed-frequency score is not “LFU with a knob”: if it were, hit rate would climb steadily as α → 0.

Withdrawn: monotone convergence onto LFU.Revision 1 claimed hit rate was monotone as α → 0 and converged exactly onto LFU. That claim is withdrawn — it was an artifact of the _pick_victim() defect. At α = 0.001 the curve reads 24.44 against LFU’s 15.56, and it is descending, not converging. The collapse at small α is a metadata-reset artifact, not a property of the scoring function.

Simulated (provisional) — CANONICAL-NUMBERS.md §3.2, experiment e2 in results_v2.json