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Equation 9 · Part 4 · How Training Data and Synthetic Data Actually Work

Symbol e^varepsilon

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
eεe^{\varepsilon}

What this part means

eve^varepsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

eve^varepsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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