Remap logprobs through the centered curve g(z), z = ℓ − μ:
toe (z < −w): −m·w − m·β_t·ln(1 + (−z − w)/β_t) gentle shadow rolloff
mid (|z| ≤ w): m·z contrast gain
shoulder(z > w): m·w + m·β_h·ln(1 + ( z − w)/β_h) highlight rolloff
Monotone in ℓ ⇒ ranking-preserving (argmax unchanged). With width = ∞ (or
β_h, β_t ≤ 0) it returns mulScalar(lp, m) — temperature T = 1/m — bit-exact
by construction (the same op the temperature path uses). -inf (masked)
tokens map to -inf.
Remap logprobs through the centered curve g(z), z = ℓ − μ: toe (z < −w): −m·w − m·β_t·ln(1 + (−z − w)/β_t) gentle shadow rolloff mid (|z| ≤ w): m·z contrast gain shoulder(z > w): m·w + m·β_h·ln(1 + ( z − w)/β_h) highlight rolloff Monotone in ℓ ⇒ ranking-preserving (argmax unchanged). With width = ∞ (or β_h, β_t ≤ 0) it returns mulScalar(lp, m) — temperature T = 1/m — bit-exact by construction (the same op the temperature path uses).
-inf(masked) tokens map to-inf.