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Equation 9 · Part 7 · How Training Data and Synthetic Data Actually Work

multiplication

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
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

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

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the surrounding passage

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