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leiden_hybrid_concepts
label: sonnet
community:leiden_hybrid_concepts-run2-c13Few-shot arithmetic learning thresholds
k50 and phase width metrics for multi-base addition across bases 8, 9, and 10
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Findings (5)
- B10 phase width Δk = 1.21 ± 0.18Transition width (k90 – k10) for B10.
- B10 shot midpoint k50 = 0.28 ± 0.05 shots with accuracy 94.8 ± 1.2%Lowest threshold condition in E2; near-zero/one-shot threshold consistent with high pretraining density
- B9 phase width (k90 − k10) = 3.74 ± 0.31 shotsWidest transition in E2; consistent with lower prior density requiring more shots for reliable threshold crossing
- k50 for base-10 two-digit addition: 0.28 ± 0.05 shotsShot midpoint from logistic fit over 10 runs.
- k50 ordering: B10 (0.28) < B8 (1.83) < B9 (2.91) follows pretraining densityMonotone ordering consistent with k50 ∝ dr/ρd.
Claims (1)
- Shot midpoint ordering k50(B10) < k50(B8) ≈ k50(B9) tracks pretraining exposure densityInterpretation that pattern density from pretraining determines few-shot requirements