Power-sharpened allocation distribution

Read the equation

Raises each nonnegative allocation to power γ and renormalizes. For γ>1 this concentrates relative mass on larger entries. The denominator must remain positive; an all-zero vector needs a fallback.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read π^eff_s as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

▼
STAGE 4: COMPETITION SHARPENING + NORMALIZE
π^eff_s = (π³_s)^γ / Σ_u(π³_u)^γ     where γ > 1

Before: [0.40, 0.30, 0.20, 0.10]
After:  [0.53, 0.30, 0.13, 0.03]     ← winner-take-more, still differentiable

▼
OUTPUT: π^eff (sparse allocation weights for master update)

π^eff_s = (π³_s)^γ / Σ_u(π³_u)^γ     where γ > 1

Related builds