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Equation 9 · Part 6 · How Training Data and Synthetic Data Actually Work

≤

Pr⁡[M(D)∈S]≤eε⋅Pr⁡[M(D′)∈S]+δ\Pr[\mathcal{M}(D) \in S] \le e^{\varepsilon} \cdot \Pr[\mathcal{M}(D') \in S] + \delta
≤

What this part means

Less than or equal to.

Its job in the formula

Less than or equal to.

The passage around this formula

The final mechanism worth separating out is synthetic data generation aimed specifically at privacy rather than capability — producing a dataset that preserves the statistical properties of a sensitive real dataset (medical records, private communications) without preserving any individual record well enough to be re-identified. The standard mechanical tool here is differential privacy, formalized by Abadi and colleagues’ DP-SGD algorithm, which modifies ordinary stochastic gradient descent by clipping each individual training example’s gradient contribution to a bounded norm and then adding calibrated random noise before the aggregated update is applied [ 9 ] . The guarantee this produces…

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Learn the underlying idea

An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

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Sources cited in the surrounding passage

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