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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

func (a *rdpAccountant) composedRDP(release GaussianRelease) []float64 · MINIMUM over the grid of epsilon(alpha)

This relation defines MINIMUM over the grid of epsilon(alpha) in the source section “func (a *rdpAccountant) composedRDP(release GaussianRelease) []float64 · MINIMUM over the grid of epsilon(alpha)”. Uses logarithmic scaling; its base and the positivity of its argument…

Implementation mathematicsSource recovered; runtime not executed
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gh-eq-f6d3599537bca2a6source-comment-equation
MINIMUMoverthegridofepsilon(alpha)=rdp(alpha)+log(1/delta)/(alpha−1).TakingtheminovertheMINIMUM over the grid of epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). Taking the min over the

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This relation defines MINIMUM over the grid of epsilon(alpha) in the source section “func (a *rdpAccountant) composedRDP(release GaussianRelease) []float64 · MINIMUM over the grid of 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

  1. Read MINIMUM over the grid of epsilon(alpha) as the quantity being defined or updated by this relation.

  2. Uses logarithmic scaling; its base and the positivity of its argument matter.

  3. 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
	for i, alpha := range a.orders {
		out[i] = gaussianRDP(sigma, alpha)
	}
	return out
}

// epsilonFor converts a per order accumulated RDP slice to the reported epsilon at the configured delta: the
// MINIMUM over the grid of epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). Taking the min over the
// grid is what makes this a valid (epsilon, delta) guarantee: an (alpha, rdp(alpha)) RDP bound implies the
// (epsilon, delta) bound at every order, so the smallest of them is the tightest sound epsilon.
//
// An empty accumulation (no releases composed, every order zero) is the zero mechanism, whose true privacy
// loss is exactly zero, so epsilonFor returns 0 rather than the positive delta slack the conversion formula
// would otherwise report at zero RDP. This matches the standard accountant convention (a fresh budget has
// spent nothing).
func (a *rdpAccountant) epsilonFor(accRDP []float64) float64 {
	allZero := true
	for _, v := range accRDP {
Exact original notation
MINIMUM over the grid of epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1). Taking the min over the

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