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This relation defines the standard closed form epsilon(alpha) in the source section “func gaussianRDP(sigma, alpha float64) float64 · the standard closed form epsilon(alpha)”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
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
Read the standard closed form epsilon(alpha) as the quantity being defined or updated by this relation.
Uses logarithmic scaling; its base and the positivity of its argument matter.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
// understate it. If a provably random participation scheme is ever adopted, the subsampled RDP bound from
// arxiv 1808.00087 would tighten this, but the no amplification curve here stays a sound upper bound.
func gaussianRDP(sigma, alpha float64) float64 {
return alpha / (2 * sigma * sigma)
}
// epsilonAtOrder converts an accumulated RDP value at one Renyi order to an (epsilon, delta) epsilon using
// the standard closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). This is the canonical
// RDP to approximate DP conversion (Mironov 2017, cited in docs/AI_RESEARCH.md). alpha must be greater than 1
// and delta must be in (0, 1).
func epsilonAtOrder(rdp, alpha, delta float64) float64 {
return rdp + math.Log(1/delta)/(alpha-1)
}
// Accountant is the privacy budget accountant boundary. Charge composes one release into the running budget
// and returns the epsilon at the configured delta after the release, or refuses it (returning
// ErrBudgetExceeded) if it would exceed the budget. Remaining returns the epsilon headroom left before the
// budget is spent. An accountant implementation may be pure (in memory, for tests and the math) or ledgerExact original notation
the standard closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). This is the canonical