Better Privacy Guarantees for Larger Groups

What the math gives to ML

The paper establishes an optimal inverse-square law for count-dependent zero-concentrated differential privacy: if a group of size n must retain fixed relative error, its privacy budget can scale as v(n)=Theta_r(n^{-2}), and no mechanism can asymptotically improve this rate. The transferable asset is a principled way to make Gaussian release noise proportional to group size rather than constant, preserving relative utility while making privacy loss decrease quadratically for large groups. This can be tested in private federated aggregation or private MoE routing statistics, although the exact theorem relies on a shifted-log Gaussian construction whose full formula is not present in the extracted text.